LMFDB - Embedded newform 315.2.be.c.236.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			236.10
Character	$\chi$	$=$	315.236
Dual form			315.2.be.c.311.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.403396 - 0.232901i) q^{2} +(0.625194 + 1.61528i) q^{3} +(-0.891514 + 1.54415i) q^{4} -1.00000 q^{5} +(0.628402 + 0.505990i) q^{6} +(-2.59662 - 0.507526i) q^{7} +1.76214i q^{8} +(-2.21827 + 2.01973i) q^{9} +O(q^{10})$	\(q+(0.403396 - 0.232901i) q^{2} +(0.625194 + 1.61528i) q^{3} +(-0.891514 + 1.54415i) q^{4} -1.00000 q^{5} +(0.628402 + 0.505990i) q^{6} +(-2.59662 - 0.507526i) q^{7} +1.76214i q^{8} +(-2.21827 + 2.01973i) q^{9} +(-0.403396 + 0.232901i) q^{10} +0.201105i q^{11} +(-3.05160 - 0.474654i) q^{12} +(0.459163 - 0.265098i) q^{13} +(-1.16567 + 0.400021i) q^{14} +(-0.625194 - 1.61528i) q^{15} +(-1.37262 - 2.37745i) q^{16} +(2.13878 + 3.70447i) q^{17} +(-0.424444 + 1.33139i) q^{18} +(-0.0968564 - 0.0559201i) q^{19} +(0.891514 - 1.54415i) q^{20} +(-0.803592 - 4.51157i) q^{21} +(0.0468375 + 0.0811248i) q^{22} +4.40192i q^{23} +(-2.84636 + 1.10168i) q^{24} +1.00000 q^{25} +(0.123483 - 0.213879i) q^{26} +(-4.64927 - 2.32040i) q^{27} +(3.09862 - 3.55709i) q^{28} +(1.21674 + 0.702487i) q^{29} +(-0.628402 - 0.505990i) q^{30} +(4.59638 + 2.65372i) q^{31} +(-4.15954 - 2.40151i) q^{32} +(-0.324840 + 0.125729i) q^{33} +(1.72555 + 0.996248i) q^{34} +(2.59662 + 0.507526i) q^{35} +(-1.14114 - 5.22595i) q^{36} +(-0.817557 + 1.41605i) q^{37} -0.0520954 q^{38} +(0.715274 + 0.575940i) q^{39} -1.76214i q^{40} +(4.47333 + 7.74803i) q^{41} +(-1.37492 - 1.63279i) q^{42} +(4.56007 - 7.89827i) q^{43} +(-0.310535 - 0.179288i) q^{44} +(2.21827 - 2.01973i) q^{45} +(1.02521 + 1.77572i) q^{46} +(4.76120 + 8.24664i) q^{47} +(2.98210 - 3.70354i) q^{48} +(6.48484 + 2.63570i) q^{49} +(0.403396 - 0.232901i) q^{50} +(-4.64662 + 5.77074i) q^{51} +0.945355i q^{52} +(-6.28821 + 3.63050i) q^{53} +(-2.41592 + 0.146780i) q^{54} -0.201105i q^{55} +(0.894333 - 4.57561i) q^{56} +(0.0297726 - 0.191411i) q^{57} +0.654440 q^{58} +(1.66764 - 2.88844i) q^{59} +(3.05160 + 0.474654i) q^{60} +(9.46329 - 5.46363i) q^{61} +2.47222 q^{62} +(6.78505 - 4.11863i) q^{63} +3.25323 q^{64} +(-0.459163 + 0.265098i) q^{65} +(-0.101757 + 0.126374i) q^{66} +(-3.95838 + 6.85611i) q^{67} -7.62701 q^{68} +(-7.11033 + 2.75205i) q^{69} +(1.16567 - 0.400021i) q^{70} -13.5304i q^{71} +(-3.55905 - 3.90890i) q^{72} +(-3.84167 + 2.21799i) q^{73} +0.761639i q^{74} +(0.625194 + 1.61528i) q^{75} +(0.172698 - 0.0997071i) q^{76} +(0.102066 - 0.522191i) q^{77} +(0.422676 + 0.0657441i) q^{78} +(-8.62845 - 14.9449i) q^{79} +(1.37262 + 2.37745i) q^{80} +(0.841400 - 8.96058i) q^{81} +(3.60905 + 2.08369i) q^{82} +(-2.64187 + 4.57586i) q^{83} +(7.68294 + 2.78126i) q^{84} +(-2.13878 - 3.70447i) q^{85} -4.24818i q^{86} +(-0.374014 + 2.40457i) q^{87} -0.354375 q^{88} +(-2.74526 + 4.75493i) q^{89} +(0.424444 - 1.33139i) q^{90} +(-1.32682 + 0.455321i) q^{91} +(-6.79721 - 3.92437i) q^{92} +(-1.41288 + 9.08353i) q^{93} +(3.84130 + 2.21778i) q^{94} +(0.0968564 + 0.0559201i) q^{95} +(1.27860 - 8.22024i) q^{96} +(0.347490 + 0.200623i) q^{97} +(3.22982 - 0.447093i) q^{98} +(-0.406176 - 0.446103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.403396	−	0.232901i	0.285244	−	0.164686i	−0.350551	−	0.936544i	$-0.614006\pi$
$2$	0.403396	−	0.232901i	0.285244	−	0.164686i	0.635795	+	0.771858i	$0.280672\pi$
$3$	0.625194	+	1.61528i	0.360956	+	0.932583i
$3$	0.625194	+	1.61528i	0.360956	+	0.932583i
$4$	−0.891514	+	1.54415i	−0.445757	+	0.772074i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.628402	+	0.505990i	0.256544	+	0.206570i
$7$	−2.59662	−	0.507526i	−0.981429	−	0.191827i
$7$	−2.59662	−	0.507526i	−0.981429	−	0.191827i
$8$			1.76214i			0.623011i
$9$	−2.21827	+	2.01973i	−0.739422	+	0.673243i
$10$	−0.403396	+	0.232901i	−0.127565	+	0.0736498i
$11$			0.201105i			0.0606353i	0.999540	+	0.0303176i	$0.00965189\pi$
$11$			0.201105i			0.0606353i	−0.999540	+	0.0303176i	$0.990348\pi$
$12$	−3.05160	−	0.474654i	−0.880922	−	0.137021i
$13$	0.459163	−	0.265098i	0.127349	−	0.0735250i	−0.434972	−	0.900444i	$-0.643242\pi$
$13$	0.459163	−	0.265098i	0.127349	−	0.0735250i	0.562321	+	0.826919i	$0.309908\pi$
$14$	−1.16567	+	0.400021i	−0.311538	+	0.106910i
$15$	−0.625194	−	1.61528i	−0.161424	−	0.417064i
$16$	−1.37262	−	2.37745i	−0.343156	−	0.594363i
$17$	2.13878	+	3.70447i	0.518730	+	0.898467i	0.999763	+	0.0217646i	$0.00692842\pi$
$17$	2.13878	+	3.70447i	0.518730	+	0.898467i	−0.481033	+	0.876703i	$0.659738\pi$
$18$	−0.424444	+	1.33139i	−0.100042	+	0.313811i
$19$	−0.0968564	−	0.0559201i	−0.0222204	−	0.0128289i	0.488849	−	0.872369i	$-0.337417\pi$
$19$	−0.0968564	−	0.0559201i	−0.0222204	−	0.0128289i	−0.511069	+	0.859540i	$0.670750\pi$
$20$	0.891514	−	1.54415i	0.199349	−	0.345282i
$21$	−0.803592	−	4.51157i	−0.175358	−	0.984505i
$22$	0.0468375	+	0.0811248i	0.00998578	+	0.0172959i
$23$			4.40192i			0.917863i	0.888472	+	0.458932i	$0.151768\pi$
$23$			4.40192i			0.917863i	−0.888472	+	0.458932i	$0.848232\pi$
$24$	−2.84636	+	1.10168i	−0.581010	+	0.224880i
$25$	1.00000			0.200000
$26$	0.123483	−	0.213879i	0.0242171	−	0.0419452i
$27$	−4.64927	−	2.32040i	−0.894753	−	0.446561i
$28$	3.09862	−	3.55709i	0.585583	−	0.672228i
$29$	1.21674	+	0.702487i	0.225944	+	0.130449i	0.608699	−	0.793401i	$-0.291692\pi$
$29$	1.21674	+	0.702487i	0.225944	+	0.130449i	−0.382756	+	0.923850i	$0.625025\pi$
$30$	−0.628402	−	0.505990i	−0.114730	−	0.0923808i
$31$	4.59638	+	2.65372i	0.825534	+	0.476622i	0.852321	−	0.523019i	$-0.175194\pi$
$31$	4.59638	+	2.65372i	0.825534	+	0.476622i	−0.0267874	+	0.999641i	$0.508528\pi$
$32$	−4.15954	−	2.40151i	−0.735310	−	0.424532i
$33$	−0.324840	+	0.125729i	−0.0565474	+	0.0218867i
$34$	1.72555	+	0.996248i	0.295930	+	0.170855i
$35$	2.59662	+	0.507526i	0.438908	+	0.0857875i
$36$	−1.14114	−	5.22595i	−0.190191	−	0.870991i
$37$	−0.817557	+	1.41605i	−0.134405	+	0.232797i	−0.925370	−	0.379065i	$-0.876246\pi$
$37$	−0.817557	+	1.41605i	−0.134405	+	0.232797i	0.790965	+	0.611862i	$0.209579\pi$
$38$	−0.0520954			−0.00845099
$39$	0.715274	+	0.575940i	0.114536	+	0.0922242i
$40$		−	1.76214i		−	0.278619i
$41$	4.47333	+	7.74803i	0.698616	+	1.21004i	0.968946	+	0.247271i	$0.0795339\pi$
$41$	4.47333	+	7.74803i	0.698616	+	1.21004i	−0.270330	+	0.962768i	$0.587133\pi$
$42$	−1.37492	−	1.63279i	−0.212154	−	0.251945i
$43$	4.56007	−	7.89827i	0.695404	−	1.20447i	−0.274641	−	0.961547i	$-0.588559\pi$
$43$	4.56007	−	7.89827i	0.695404	−	1.20447i	0.970044	−	0.242927i	$-0.0781077\pi$
$44$	−0.310535	−	0.179288i	−0.0468149	−	0.0270286i
$45$	2.21827	−	2.01973i	0.330679	−	0.301083i
$46$	1.02521	+	1.77572i	0.151159	+	0.261815i
$47$	4.76120	+	8.24664i	0.694492	+	1.20290i	0.970352	+	0.241698i	$0.0777042\pi$
$47$	4.76120	+	8.24664i	0.694492	+	1.20290i	−0.275859	+	0.961198i	$0.588962\pi$
$48$	2.98210	−	3.70354i	0.430429	−	0.534560i
$49$	6.48484	+	2.63570i	0.926405	+	0.376528i
$50$	0.403396	−	0.232901i	0.0570489	−	0.0329372i
$51$	−4.64662	+	5.77074i	−0.650656	+	0.808066i
$52$			0.945355i			0.131097i
$53$	−6.28821	+	3.63050i	−0.863753	+	0.498688i	−0.865267	−	0.501311i	$-0.832851\pi$
$53$	−6.28821	+	3.63050i	−0.863753	+	0.498688i	0.00151458	+	0.999999i	$0.499518\pi$
$54$	−2.41592	+	0.146780i	−0.328766	+	0.0199742i
$55$		−	0.201105i		−	0.0271169i
$56$	0.894333	−	4.57561i	0.119510	−	0.611441i
$57$	0.0297726	−	0.191411i	0.00394348	−	0.0253530i
$58$	0.654440			0.0859322
$59$	1.66764	−	2.88844i	0.217108	−	0.376043i	−0.736814	−	0.676095i	$-0.763671\pi$
$59$	1.66764	−	2.88844i	0.217108	−	0.376043i	0.953923	+	0.300052i	$0.0970041\pi$
$60$	3.05160	+	0.474654i	0.393960	+	0.0612776i
$61$	9.46329	−	5.46363i	1.21165	−	0.699546i	0.248531	−	0.968624i	$-0.420052\pi$
$61$	9.46329	−	5.46363i	1.21165	−	0.699546i	0.963119	+	0.269077i	$0.0867188\pi$
$62$	2.47222			0.313972
$63$	6.78505	−	4.11863i	0.854836	−	0.518899i
$64$	3.25323			0.406654
$65$	−0.459163	+	0.265098i	−0.0569522	+	0.0328814i
$66$	−0.101757	+	0.126374i	−0.0125254	+	0.0155556i
$67$	−3.95838	+	6.85611i	−0.483593	+	0.837607i	−0.999822	−	0.0188429i	$-0.994002\pi$
$67$	−3.95838	+	6.85611i	−0.483593	+	0.837607i	0.516230	+	0.856450i	$0.327335\pi$
$68$	−7.62701			−0.924911
$69$	−7.11033	+	2.75205i	−0.855983	+	0.331308i
$70$	1.16567	−	0.400021i	0.139324	−	0.0478116i
$71$		−	13.5304i		−	1.60576i	−0.596140	−	0.802880i	$-0.703300\pi$
$71$		−	13.5304i		−	1.60576i	0.596140	−	0.802880i	$-0.296700\pi$
$72$	−3.55905	−	3.90890i	−0.419438	−	0.460668i
$73$	−3.84167	+	2.21799i	−0.449633	+	0.259596i	−0.707675	−	0.706538i	$-0.750256\pi$
$73$	−3.84167	+	2.21799i	−0.449633	+	0.259596i	0.258042	+	0.966134i	$0.416923\pi$
$74$			0.761639i			0.0885388i
$75$	0.625194	+	1.61528i	0.0721912	+	0.186517i
$76$	0.172698	−	0.0997071i	0.0198098	−	0.0114372i
$77$	0.102066	−	0.522191i	0.0116315	−	0.0595092i
$78$	0.422676	+	0.0657441i	0.0478586	+	0.00744406i
$79$	−8.62845	−	14.9449i	−0.970776	−	1.68143i	−0.693222	−	0.720724i	$-0.743810\pi$
$79$	−8.62845	−	14.9449i	−0.970776	−	1.68143i	−0.277554	−	0.960710i	$-0.589524\pi$
$80$	1.37262	+	2.37745i	0.153464	+	0.265807i
$81$	0.841400	−	8.96058i	0.0934889	−	0.995620i
$82$	3.60905	+	2.08369i	0.398553	+	0.230105i
$83$	−2.64187	+	4.57586i	−0.289983	+	0.502266i	−0.973805	−	0.227383i	$-0.926983\pi$
$83$	−2.64187	+	4.57586i	−0.289983	+	0.502266i	0.683822	+	0.729649i	$0.260316\pi$
$84$	7.68294	+	2.78126i	0.838278	+	0.303460i
$85$	−2.13878	−	3.70447i	−0.231983	−	0.401807i
$86$		−	4.24818i		−	0.458093i
$87$	−0.374014	+	2.40457i	−0.0400985	+	0.257797i
$88$	−0.354375			−0.0377765
$89$	−2.74526	+	4.75493i	−0.290997	+	0.504022i	−0.974046	−	0.226351i	$-0.927320\pi$
$89$	−2.74526	+	4.75493i	−0.290997	+	0.504022i	0.683049	+	0.730373i	$0.260654\pi$
$90$	0.424444	−	1.33139i	0.0447403	−	0.140341i
$91$	−1.32682	+	0.455321i	−0.139088	+	0.0477306i
$92$	−6.79721	−	3.92437i	−0.708658	−	0.409144i
$93$	−1.41288	+	9.08353i	−0.146508	+	0.941918i
$94$	3.84130	+	2.21778i	0.396200	+	0.228746i
$95$	0.0968564	+	0.0559201i	0.00993726	+	0.00573728i
$96$	1.27860	−	8.22024i	0.130496	−	0.838975i
$97$	0.347490	+	0.200623i	0.0352822	+	0.0203702i	0.517537	−	0.855661i	$-0.326849\pi$
$97$	0.347490	+	0.200623i	0.0352822	+	0.0203702i	−0.482255	+	0.876031i	$0.660182\pi$
$98$	3.22982	−	0.447093i	0.326261	−	0.0451632i
$99$	−0.406176	−	0.446103i	−0.0408223	−	0.0448351i
$100$	−0.891514	+	1.54415i	−0.0891514	+	0.154415i
$101$	8.29113			0.824998			0.412499	−	0.910958i	$-0.364656\pi$
$101$	8.29113			0.824998			0.412499	+	0.910958i	$0.364656\pi$
$102$	−0.530416	+	3.41010i	−0.0525190	+	0.337650i
$103$		−	18.9801i		−	1.87016i	−0.354430	−	0.935082i	$-0.615325\pi$
$103$		−	18.9801i		−	1.87016i	0.354430	−	0.935082i	$-0.384675\pi$
$104$	0.467141	+	0.809111i	0.0458069	+	0.0793399i
$105$	0.803592	+	4.51157i	0.0784226	+	0.440284i
$106$	−1.69110	+	2.92906i	−0.164254	+	0.284496i
$107$	5.33592	+	3.08069i	0.515843	+	0.297822i	0.735232	−	0.677815i	$-0.237073\pi$
$107$	5.33592	+	3.08069i	0.515843	+	0.297822i	−0.219389	+	0.975637i	$0.570406\pi$
$108$	7.72793	−	5.11050i	0.743621	−	0.491758i
$109$	−0.638147	−	1.10530i	−0.0611234	−	0.105869i	0.833844	−	0.552000i	$-0.186135\pi$
$109$	−0.638147	−	1.10530i	−0.0611234	−	0.105869i	−0.894968	+	0.446131i	$0.852802\pi$
$110$	−0.0468375	−	0.0811248i	−0.00446578	−	0.00773495i
$111$	−2.79845	−	0.435278i	−0.265617	−	0.0413148i
$112$	2.35756	+	6.86998i	0.222768	+	0.649152i
$113$	−12.3754	+	7.14494i	−1.16418	+	0.672140i	−0.952302	−	0.305156i	$-0.901291\pi$
$113$	−12.3754	+	7.14494i	−1.16418	+	0.672140i	−0.211878	+	0.977296i	$0.567958\pi$
$114$	−0.0325697	−	0.0841487i	−0.00305043	−	0.00788125i
$115$		−	4.40192i		−	0.410481i
$116$	−2.16949	+	1.25255i	−0.201432	+	0.116297i
$117$	−0.483120	+	1.51544i	−0.0446645	+	0.140103i
$118$		−	1.55358i		−	0.143019i
$119$	−3.67347	−	10.7046i	−0.336747	−	0.981288i
$120$	2.84636	−	1.10168i	0.259835	−	0.100569i
$121$	10.9596			0.996323
$122$	2.54497	−	4.40802i	0.230411	−	0.399083i
$123$	−9.71855	+	12.0697i	−0.876292	+	1.08829i
$124$	−8.19547	+	4.73166i	−0.735975	+	0.424915i
$125$	−1.00000			−0.0894427
$126$	1.77783	−	3.24169i	0.158382	−	0.288792i
$127$	−16.4817			−1.46251			−0.731255	−	0.682104i	$-0.761065\pi$
$127$	−16.4817			−1.46251			−0.731255	+	0.682104i	$0.761065\pi$
$128$	9.63143	−	5.56071i	0.851306	−	0.491502i
$129$	15.6088	+	2.42784i	1.37428	+	0.213759i
$130$	−0.123483	+	0.213879i	−0.0108302	+	0.0187585i
$131$	18.8252			1.64477			0.822383	−	0.568934i	$-0.192644\pi$
$131$	18.8252			1.64477			0.822383	+	0.568934i	$0.192644\pi$
$132$	0.0954551	−	0.613691i	0.00830830	−	0.0534149i
$133$	0.223118	+	0.194360i	0.0193468	+	0.0168532i
$134$			3.68764i			0.318564i
$135$	4.64927	+	2.32040i	0.400146	+	0.199708i
$136$	−6.52781	+	3.76883i	−0.559755	+	0.323175i
$137$			13.6637i			1.16737i	0.811980	+	0.583685i	$0.198390\pi$
$137$			13.6637i			1.16737i	−0.811980	+	0.583685i	$0.801610\pi$
$138$	−2.22733	+	2.76617i	−0.189603	+	0.235472i
$139$	−2.26987	+	1.31051i	−0.192528	+	0.111156i	−0.593165	−	0.805081i	$-0.702122\pi$
$139$	−2.26987	+	1.31051i	−0.192528	+	0.111156i	0.400638	+	0.916237i	$0.368789\pi$
$140$	−3.09862	+	3.55709i	−0.261881	+	0.300629i
$141$	−10.3440	+	12.8464i	−0.871119	+	1.08186i
$142$	−3.15124	−	5.45811i	−0.264446	−	0.458034i
$143$	0.0533124	+	0.0923398i	0.00445821	+	0.00772184i
$144$	7.84665	+	2.50150i	0.653888	+	0.208458i
$145$	−1.21674	−	0.702487i	−0.101045	−	0.0583384i
$146$	−1.03314	+	1.78946i	−0.0855036	+	0.148097i
$147$	−0.203115	+	12.1227i	−0.0167526	+	0.999860i
$148$	−1.45773	−	2.52486i	−0.119824	−	0.207542i
$149$		−	5.77258i		−	0.472909i	−0.971643	−	0.236454i	$-0.924015\pi$
$149$		−	5.77258i		−	0.472909i	0.971643	−	0.236454i	$-0.0759853\pi$
$150$	0.628402	+	0.505990i	0.0513088	+	0.0413139i
$151$	−10.1336			−0.824660			−0.412330	−	0.911035i	$-0.635285\pi$
$151$	−10.1336			−0.824660			−0.412330	+	0.911035i	$0.635285\pi$
$152$	0.0985392	−	0.170675i	0.00799258	−	0.0138436i
$153$	−12.2264	−	3.89775i	−0.988447	−	0.315115i
$154$	−0.0804460	−	0.234421i	−0.00648252	−	0.0188902i
$155$	−4.59638	−	2.65372i	−0.369190	−	0.213152i
$156$	−1.52701	+	0.591030i	−0.122259	+	0.0473203i
$157$	17.6719	+	10.2029i	1.41037	+	0.814279i	0.995423	−	0.0955659i	$-0.0304661\pi$
$157$	17.6719	+	10.2029i	1.41037	+	0.814279i	0.414949	+	0.909845i	$0.363799\pi$
$158$	−6.96137	−	4.01915i	−0.553817	−	0.319746i
$159$	−9.79563	−	7.88746i	−0.776844	−	0.625517i
$160$	4.15954	+	2.40151i	0.328841	+	0.189856i
$161$	2.23409	−	11.4301i	0.176071	−	0.900817i
$162$	−1.74751	−	3.81063i	−0.137297	−	0.299391i
$163$	−11.2989	+	19.5703i	−0.884998	+	1.53286i	−0.0392824	+	0.999228i	$0.512507\pi$
$163$	−11.2989	+	19.5703i	−0.884998	+	1.53286i	−0.845716	+	0.533634i	$0.820826\pi$
$164$	−15.9521			−1.24565
$165$	0.324840	−	0.125729i	0.0252888	−	0.00978802i
$166$			2.46118i			0.191025i
$167$	−2.45667	−	4.25507i	−0.190103	−	0.329267i	0.755181	−	0.655516i	$-0.227549\pi$
$167$	−2.45667	−	4.25507i	−0.190103	−	0.329267i	−0.945284	+	0.326248i	$0.894215\pi$
$168$	7.95002	−	1.41604i	0.613358	−	0.109250i
$169$	−6.35945	+	11.0149i	−0.489188	+	0.847299i
$170$	−1.72555	−	0.996248i	−0.132344	−	0.0764087i
$171$	0.327797	−	0.0715780i	0.0250672	−	0.00547371i
$172$	8.13073	+	14.0828i	0.619962	+	1.07381i
$173$	2.91058	+	5.04127i	0.221287	+	0.383281i	0.955199	−	0.295964i	$-0.0956408\pi$
$173$	2.91058	+	5.04127i	0.221287	+	0.383281i	−0.733912	+	0.679245i	$0.762307\pi$
$174$	0.409152	+	1.05710i	0.0310177	+	0.0801389i
$175$	−2.59662	−	0.507526i	−0.196286	−	0.0383653i
$176$	0.478117	−	0.276041i	0.0360394	−	0.0208074i
$177$	5.70824	+	0.887875i	0.429058	+	0.0667367i
$178$			2.55750i			0.191693i
$179$	4.85929	−	2.80551i	0.363200	−	0.209694i	−0.307283	−	0.951618i	$-0.599420\pi$
$179$	4.85929	−	2.80551i	0.363200	−	0.209694i	0.670484	+	0.741924i	$0.266087\pi$
$180$	1.14114	+	5.22595i	0.0850558	+	0.389519i
$181$			2.48235i			0.184512i	0.995735	+	0.0922558i	$0.0294078\pi$
$181$			2.48235i			0.184512i	−0.995735	+	0.0922558i	$0.970592\pi$
$182$	−0.429188	+	0.492691i	−0.0318135	+	0.0365207i
$183$	14.7417	+	11.8700i	1.08974	+	0.877459i
$184$	−7.75680			−0.571839
$185$	0.817557	−	1.41605i	0.0601080	−	0.104110i
$186$	1.54561	+	3.99332i	0.113330	+	0.292805i
$187$	−0.744987	+	0.430118i	−0.0544788	+	0.0314534i
$188$	−16.9787			−1.23830
$189$	10.8947	+	8.38481i	0.792474	+	0.609906i
$190$	0.0520954			0.00377940
$191$	8.32696	−	4.80757i	0.602518	−	0.347864i	−0.167514	−	0.985870i	$-0.553574\pi$
$191$	8.32696	−	4.80757i	0.602518	−	0.347864i	0.770031	+	0.638006i	$0.220240\pi$
$192$	2.03390	+	5.25489i	0.146784	+	0.379239i
$193$	6.43096	−	11.1387i	0.462911	−	0.801785i	−0.536194	−	0.844095i	$-0.680138\pi$
$193$	6.43096	−	11.1387i	0.462911	−	0.801785i	0.999105	+	0.0423102i	$0.0134718\pi$
$194$	0.186901			0.0134187
$195$	−0.715274	−	0.575940i	−0.0512218	−	0.0412439i
$196$	−9.85123	+	7.66378i	−0.703659	+	0.547413i
$197$		−	16.8444i		−	1.20011i	−0.799958	−	0.600056i	$-0.795145\pi$
$197$		−	16.8444i		−	1.20011i	0.799958	−	0.600056i	$-0.204855\pi$
$198$	−0.267748	−	0.0853575i	−0.0190280	−	0.00606609i
$199$	−11.1869	+	6.45878i	−0.793021	+	0.457851i	−0.841025	−	0.540996i	$-0.818047\pi$
$199$	−11.1869	+	6.45878i	−0.793021	+	0.457851i	0.0480042	+	0.998847i	$0.484714\pi$
$200$			1.76214i			0.124602i
$201$	−13.5493	−	2.10749i	−0.955694	−	0.148651i
$202$	3.34461	−	1.93101i	0.235326	−	0.135866i
$203$	−2.80289	−	2.44162i	−0.196724	−	0.171368i
$204$	−4.76836	−	12.3198i	−0.333852	−	0.862556i
$205$	−4.47333	−	7.74803i	−0.312431	−	0.541146i
$206$	−4.42049	−	7.65650i	−0.307990	−	0.533454i
$207$	−8.89067	−	9.76462i	−0.617944	−	0.678688i
$208$	−1.26052	−	0.727760i	−0.0874011	−	0.0504611i
$209$	0.0112458	−	0.0194783i	0.000777887	−	0.00134734i
$210$	1.37492	+	1.63279i	0.0948781	+	0.112673i
$211$	8.62074	+	14.9316i	0.593476	+	1.02793i	0.993760	+	0.111540i	$0.0355782\pi$
$211$	8.62074	+	14.9316i	0.593476	+	1.02793i	−0.400284	+	0.916391i	$0.631088\pi$
$212$		−	12.9466i		−	0.889174i
$213$	21.8554	−	8.45911i	1.49750	−	0.579609i
$214$	2.86999			0.196188
$215$	−4.56007	+	7.89827i	−0.310994	+	0.538657i
$216$	4.08888	−	8.19268i	0.278213	−	0.557441i
$217$	−10.5882	−	9.22347i	−0.718774	−	0.626130i
$218$	−0.514852	−	0.297250i	−0.0348702	−	0.0201323i
$219$	−5.98446	−	4.81870i	−0.404392	−	0.325618i
$220$	0.310535	+	0.179288i	0.0209363	+	0.0120876i
$221$	1.96410	+	1.13397i	0.132120	+	0.0762793i
$222$	−1.23026	+	0.476172i	−0.0825697	+	0.0319586i
$223$	1.26523	+	0.730484i	0.0847264	+	0.0489168i	0.541765	−	0.840530i	$-0.317756\pi$
$223$	1.26523	+	0.730484i	0.0847264	+	0.0489168i	−0.457038	+	0.889447i	$0.651090\pi$
$224$	9.58191	+	8.34688i	0.640218	+	0.557700i
$225$	−2.21827	+	2.01973i	−0.147884	+	0.134649i
$226$	−3.32813	+	5.76449i	−0.221384	+	0.383448i
$227$	−19.5931			−1.30044			−0.650220	−	0.759746i	$-0.725323\pi$
$227$	−19.5931			−1.30044			−0.650220	+	0.759746i	$0.725323\pi$
$228$	0.269025	+	0.216619i	0.0178166	+	0.0143460i
$229$		−	18.9292i		−	1.25088i	−0.780272	−	0.625440i	$-0.784920\pi$
$229$		−	18.9292i		−	1.25088i	0.780272	−	0.625440i	$-0.215080\pi$
$230$	−1.02521	−	1.77572i	−0.0676004	−	0.117087i
$231$	0.907297	−	0.161606i	0.0596957	−	0.0106329i
$232$	−1.23788	+	2.14408i	−0.0812710	+	0.140765i
$233$	7.40865	+	4.27738i	0.485357	+	0.280221i	0.722646	−	0.691218i	$-0.242926\pi$
$233$	7.40865	+	4.27738i	0.485357	+	0.280221i	−0.237290	+	0.971439i	$0.576259\pi$
$234$	0.158059	+	0.723843i	0.0103327	+	0.0473191i
$235$	−4.76120	−	8.24664i	−0.310586	−	0.537951i
$236$	2.97345	+	5.15017i	0.193555	+	0.335248i
$237$	18.7458	−	23.2808i	1.21767	−	1.51225i
$238$	−3.97498	−	3.46264i	−0.257659	−	0.224449i
$239$	20.3636	−	11.7569i	1.31721	−	0.760492i	0.333931	−	0.942598i	$-0.391625\pi$
$239$	20.3636	−	11.7569i	1.31721	−	0.760492i	0.983279	+	0.182106i	$0.0582914\pi$
$240$	−2.98210	+	3.70354i	−0.192494	+	0.239063i
$241$			21.9551i			1.41425i	0.707086	+	0.707127i	$0.250009\pi$
$241$			21.9551i			1.41425i	−0.707086	+	0.707127i	$0.749991\pi$
$242$	4.42105	−	2.55249i	0.284196	−	0.164080i
$243$	14.9999	−	4.24300i	0.962244	−	0.272189i
$244$			19.4836i			1.24731i
$245$	−6.48484	−	2.63570i	−0.414301	−	0.168389i
$246$	−1.10938	+	7.13234i	−0.0707316	+	0.454741i
$247$	−0.0592972			−0.00377299
$248$	−4.67623	+	8.09947i	−0.296941	+	0.514317i
$249$	−9.04298	−	1.40657i	−0.573076	−	0.0891376i
$250$	−0.403396	+	0.232901i	−0.0255130	+	0.0147300i
$251$	−10.2217			−0.645188			−0.322594	−	0.946537i	$-0.604555\pi$
$251$	−10.2217			−0.645188			−0.322594	+	0.946537i	$0.604555\pi$
$252$	0.310811	+	14.1489i	0.0195792	+	0.891299i
$253$	−0.885245			−0.0556549
$254$	−6.64864	+	3.83860i	−0.417173	+	0.240855i
$255$	4.64662	−	5.77074i	0.290982	−	0.361378i
$256$	−0.663045	+	1.14843i	−0.0414403	+	0.0717767i
$257$	20.2107			1.26071			0.630355	−	0.776307i	$-0.282909\pi$
$257$	20.2107			1.26071			0.630355	+	0.776307i	$0.282909\pi$
$258$	6.86200	−	2.65593i	0.427209	−	0.165351i
$259$	2.84156	−	3.26201i	0.176566	−	0.202691i
$260$		−	0.945355i		−	0.0586284i
$261$	−4.11789	+	0.899188i	−0.254891	+	0.0556583i
$262$	7.59402	−	4.38441i	0.469160	−	0.270870i
$263$		−	4.47990i		−	0.276243i	−0.990415	−	0.138121i	$-0.955894\pi$
$263$		−	4.47990i		−	0.276243i	0.990415	−	0.138121i	$-0.0441064\pi$
$264$	−0.221553	−	0.572415i	−0.0136356	−	0.0352297i
$265$	6.28821	−	3.63050i	0.386282	−	0.223020i
$266$	0.135272	+	0.0264397i	0.00829404	+	0.00162112i
$267$	−9.39687	−	1.46161i	−0.575079	−	0.0894493i
$268$	−7.05790	−	12.2246i	−0.431130	−	0.746739i
$269$	−3.86772	−	6.69908i	−0.235819	−	0.408450i	0.723691	−	0.690124i	$-0.242444\pi$
$269$	−3.86772	−	6.69908i	−0.235819	−	0.408450i	−0.959510	+	0.281673i	$0.909111\pi$
$270$	2.41592	−	0.146780i	0.147028	−	0.00893272i
$271$	4.08240	+	2.35697i	0.247988	+	0.143176i	0.618843	−	0.785515i	$-0.287602\pi$
$271$	4.08240	+	2.35697i	0.247988	+	0.143176i	−0.370855	+	0.928691i	$0.620935\pi$
$272$	5.87148	−	10.1697i	0.356011	−	0.616629i
$273$	−1.56499	−	1.85852i	−0.0947174	−	0.112482i
$274$	3.18229	+	5.51190i	0.192249	+	0.332986i
$275$			0.201105i			0.0121271i
$276$	2.08939	−	13.4329i	0.125766	−	0.808565i
$277$	7.52737			0.452276			0.226138	−	0.974095i	$-0.427390\pi$
$277$	7.52737			0.452276			0.226138	+	0.974095i	$0.427390\pi$
$278$	−0.610438	+	1.05731i	−0.0366116	+	0.0634132i
$279$	−15.5558	+	3.39678i	−0.931300	+	0.203360i
$280$	−0.894333	+	4.57561i	−0.0534466	+	0.273445i
$281$	−4.37294	−	2.52472i	−0.260868	−	0.150612i	0.363863	−	0.931453i	$-0.381458\pi$
$281$	−4.37294	−	2.52472i	−0.260868	−	0.150612i	−0.624730	+	0.780841i	$0.714791\pi$
$282$	−1.18077	+	7.59132i	−0.0703140	+	0.452057i
$283$	−5.37060	−	3.10072i	−0.319249	−	0.184318i	0.331809	−	0.943347i	$-0.392341\pi$
$283$	−5.37060	−	3.10072i	−0.319249	−	0.184318i	−0.651058	+	0.759028i	$0.725674\pi$
$284$	20.8929	+	12.0625i	1.23977	+	0.715779i
$285$	−0.0297726	+	0.191411i	−0.00176358	+	0.0113382i
$286$	0.0430121	+	0.0248330i	0.00254336	+	0.00146841i
$287$	−7.68319	−	22.3890i	−0.453524	−	1.32158i
$288$	14.0774	−	3.07395i	0.829517	−	0.181134i
$289$	−0.648755	+	1.12368i	−0.0381621	+	0.0660987i
$290$	−0.654440			−0.0384300
$291$	−0.106815	+	0.686722i	−0.00626158	+	0.0402564i
$292$		−	7.90947i		−	0.462867i
$293$	8.96553	+	15.5288i	0.523772	+	0.907199i	0.999617	+	0.0276703i	$0.00880886\pi$
$293$	8.96553	+	15.5288i	0.523772	+	0.907199i	−0.475845	+	0.879529i	$0.657858\pi$
$294$	2.74144	+	4.93754i	0.159884	+	0.287963i
$295$	−1.66764	+	2.88844i	−0.0970938	+	0.168171i
$296$	−2.49528	−	1.44065i	−0.145035	−	0.0837362i
$297$	0.466643	−	0.934990i	0.0270774	−	0.0542536i
$298$	−1.34444	−	2.32864i	−0.0778814	−	0.134894i
$299$	1.16694	+	2.02120i	0.0674859	+	0.116889i
$300$	−3.05160	−	0.474654i	−0.176184	−	0.0274042i
$301$	−15.8493	+	18.1944i	−0.913539	+	1.04871i
$302$	−4.08786	+	2.36012i	−0.235230	+	0.135810i
$303$	5.18356	+	13.3925i	0.297788	+	0.769379i
$304$			0.307029i			0.0176093i
$305$	−9.46329	+	5.46363i	−0.541866	+	0.312847i
$306$	−5.83988	+	1.27520i	−0.333844	+	0.0728985i
$307$		−	26.4532i		−	1.50976i	−0.655861	−	0.754882i	$-0.727694\pi$
$307$		−	26.4532i		−	1.50976i	0.655861	−	0.754882i	$-0.272306\pi$
$308$	0.715348	+	0.623146i	0.0407607	+	0.0355070i
$309$	30.6582	−	11.8662i	1.74408	−	0.675047i
$310$	−2.47222			−0.140412
$311$	−4.20265	+	7.27921i	−0.238311	+	0.412766i	−0.960230	−	0.279212i	$-0.909927\pi$
$311$	−4.20265	+	7.27921i	−0.238311	+	0.412766i	0.721919	+	0.691977i	$0.243260\pi$
$312$	−1.01489	+	1.26041i	−0.0574568	+	0.0713569i
$313$	25.9979	−	15.0099i	1.46949	−	0.848411i	0.470076	−	0.882626i	$-0.344226\pi$
$313$	25.9979	−	15.0099i	1.46949	−	0.848411i	0.999415	+	0.0342148i	$0.0108930\pi$
$314$	9.50505			0.536401
$315$	−6.78505	+	4.11863i	−0.382294	+	0.232059i
$316$	30.7695			1.73092
$317$	14.1941	−	8.19496i	0.797219	−	0.460275i	−0.0452788	−	0.998974i	$-0.514418\pi$
$317$	14.1941	−	8.19496i	0.797219	−	0.460275i	0.842498	+	0.538700i	$0.181084\pi$
$318$	−5.78852	−	0.900362i	−0.324604	−	0.0504898i
$319$	−0.141273	+	0.244693i	−0.00790979	+	0.0137002i
$320$	−3.25323			−0.181861
$321$	−1.64020	+	10.5450i	−0.0915472	+	0.588567i
$322$	−1.76086	−	5.13118i	−0.0981288	−	0.285949i
$323$		−	0.478403i		−	0.0266191i
$324$	13.0863	+	9.28773i	0.727019	+	0.515985i
$325$	0.459163	−	0.265098i	0.0254698	−	0.0147050i
$326$			10.5261i			0.582987i
$327$	1.38641	−	1.72181i	0.0766686	−	0.0952166i
$328$	−13.6531	+	7.88264i	−0.753868	+	0.435246i
$329$	−8.17763	−	23.8298i	−0.450847	−	1.31378i
$330$	0.101757	−	0.126374i	0.00560153	−	0.00695668i
$331$	−10.1069	−	17.5057i	−0.555527	−	0.962201i	−0.997862	−	0.0653516i	$-0.979183\pi$
$331$	−10.1069	−	17.5057i	−0.555527	−	0.962201i	0.442335	−	0.896850i	$-0.354150\pi$
$332$	−4.71053	−	8.15889i	−0.258524	−	0.447777i
$333$	−1.04648	−	4.79242i	−0.0573466	−	0.262623i
$334$	−1.98202	−	1.14432i	−0.108451	−	0.0626145i
$335$	3.95838	−	6.85611i	0.216269	−	0.374589i
$336$	−9.62301	+	8.10319i	−0.524978	+	0.442065i
$337$	−3.32447	−	5.75815i	−0.181095	−	0.313667i	0.761158	−	0.648566i	$-0.224631\pi$
$337$	−3.32447	−	5.75815i	−0.181095	−	0.313667i	−0.942254	+	0.334899i	$0.891298\pi$
$338$			5.92449i			0.322250i
$339$	−19.2781	−	15.5228i	−1.04704	−	0.843082i
$340$	7.62701			0.413633
$341$	−0.533675	+	0.924352i	−0.0289001	+	0.0500565i
$342$	0.115561	−	0.105219i	0.00624884	−	0.00568957i
$343$	−15.5009	−	10.1351i	−0.836972	−	0.547245i
$344$	13.9179	+	8.03549i	0.750401	+	0.433244i
$345$	7.11033	−	2.75205i	0.382807	−	0.148165i
$346$	2.34824	+	1.35575i	0.126242	+	0.0728858i
$347$	14.1890	+	8.19204i	0.761707	+	0.439772i	0.829908	−	0.557900i	$-0.188393\pi$
$347$	14.1890	+	8.19204i	0.761707	+	0.439772i	−0.0682011	+	0.997672i	$0.521726\pi$
$348$	−3.37958	−	2.72124i	−0.181164	−	0.145874i
$349$	25.2067	+	14.5531i	1.34928	+	0.779008i	0.988148	−	0.153506i	$-0.0490565\pi$
$349$	25.2067	+	14.5531i	1.34928	+	0.779008i	0.361134	+	0.932514i	$0.382390\pi$
$350$	−1.16567	+	0.400021i	−0.0623076	+	0.0213820i
$351$	−2.74991	+	0.167071i	−0.146779	+	0.00891759i
$352$	0.482955	−	0.836503i	0.0257416	−	0.0445858i
$353$	−9.58101			−0.509946			−0.254973	−	0.966948i	$-0.582067\pi$
$353$	−9.58101			−0.509946			−0.254973	+	0.966948i	$0.582067\pi$
$354$	2.50947	−	0.971290i	0.133377	−	0.0516235i
$355$			13.5304i			0.718118i
$356$	−4.89488	−	8.47818i	−0.259428	−	0.449343i
$357$	14.9943	−	12.6261i	0.793581	−	0.668246i
$358$	1.30681	−	2.26347i	0.0690672	−	0.119628i
$359$	22.1206	+	12.7713i	1.16748	+	0.674045i	0.953085	−	0.302703i	$-0.0978889\pi$
$359$	22.1206	+	12.7713i	1.16748	+	0.674045i	0.214394	+	0.976747i	$0.431222\pi$
$360$	3.55905	+	3.90890i	0.187578	+	0.206017i
$361$	−9.49375	−	16.4437i	−0.499671	−	0.865455i
$362$	0.578142	+	1.00137i	0.0303865	+	0.0526309i
$363$	6.85185	+	17.7028i	0.359629	+	0.929154i
$364$	0.479792	−	2.45472i	0.0251479	−	0.128663i
$365$	3.84167	−	2.21799i	0.201082	−	0.116095i
$366$	8.71129	+	1.35498i	0.455346	+	0.0708258i
$367$		−	5.87902i		−	0.306882i	−0.988158	−	0.153441i	$-0.950964\pi$
$367$		−	5.87902i		−	0.306882i	0.988158	−	0.153441i	$-0.0490355\pi$
$368$	10.4654	−	6.04217i	0.545544	−	0.314970i
$369$	−25.5719	−	8.15228i	−1.33122	−	0.424391i
$370$		−	0.761639i		−	0.0395957i
$371$	18.1707	−	6.23559i	0.943373	−	0.323736i
$372$	−12.7667	−	10.2798i	−0.661923	−	0.532982i
$373$	0.296837			0.0153697			0.00768483	−	0.999970i	$-0.497554\pi$
$373$	0.296837			0.0153697			0.00768483	+	0.999970i	$0.497554\pi$
$374$	−0.200350	+	0.347016i	−0.0103599	+	0.0179438i
$375$	−0.625194	−	1.61528i	−0.0322849	−	0.0834127i
$376$	−14.5317	+	8.38991i	−0.749418	+	0.432677i
$377$	0.744912			0.0383649
$378$	6.34772	+	0.845013i	0.326492	+	0.0434628i
$379$	13.7691			0.707269			0.353635	−	0.935384i	$-0.384946\pi$
$379$	13.7691			0.707269			0.353635	+	0.935384i	$0.384946\pi$
$380$	−0.172698	+	0.0997071i	−0.00885921	+	0.00511487i
$381$	−10.3042	−	26.6225i	−0.527902	−	1.36391i
$382$	2.23938	−	3.87872i	0.114577	−	0.198452i
$383$	−37.7706			−1.92999			−0.964995	−	0.262269i	$-0.915529\pi$
$383$	−37.7706			−1.92999			−0.964995	+	0.262269i	$0.915529\pi$
$384$	15.0036	+	12.0809i	0.765650	+	0.616503i
$385$	−0.102066	+	0.522191i	−0.00520175	+	0.0266133i
$386$		−	5.99111i		−	0.304939i
$387$	5.83691	+	26.7305i	0.296707	+	1.35879i
$388$	−0.619584	+	0.357717i	−0.0314546	+	0.0181603i
$389$		−	20.3600i		−	1.03229i	−0.856501	−	0.516146i	$-0.827366\pi$
$389$		−	20.3600i		−	1.03229i	0.856501	−	0.516146i	$-0.172634\pi$
$390$	−0.422676	−	0.0657441i	−0.0214030	−	0.00332908i
$391$	−16.3068	+	9.41473i	−0.824670	+	0.476123i
$392$	−4.64448	+	11.4272i	−0.234582	+	0.577161i
$393$	11.7694	+	30.4080i	0.593688	+	1.53388i
$394$	−3.92308	−	6.79497i	−0.197642	−	0.342325i
$395$	8.62845	+	14.9449i	0.434144	+	0.751960i
$396$	1.05096	−	0.229489i	0.0528128	−	0.0115323i
$397$	13.3235	+	7.69232i	0.668687	+	0.386067i	0.795579	−	0.605850i	$-0.207167\pi$
$397$	13.3235	+	7.69232i	0.668687	+	0.386067i	−0.126892	+	0.991917i	$0.540500\pi$
$398$	−3.00851	+	5.21090i	−0.150803	+	0.261199i
$399$	−0.174454	+	0.481911i	−0.00873363	+	0.0241257i
$400$	−1.37262	−	2.37745i	−0.0686312	−	0.118873i
$401$			8.42820i			0.420884i	0.977606	+	0.210442i	$0.0674904\pi$
$401$			8.42820i			0.420884i	−0.977606	+	0.210442i	$0.932510\pi$
$402$	−5.95658	+	2.30549i	−0.297087	+	0.114987i
$403$	2.81398			0.140175
$404$	−7.39166	+	12.8027i	−0.367749	+	0.636960i
$405$	−0.841400	+	8.96058i	−0.0418095	+	0.445255i
$406$	−1.69933	−	0.332145i	−0.0843363	−	0.0164841i
$407$	−0.284774	−	0.164414i	−0.0141157	−	0.00814972i
$408$	−10.1689	−	8.18800i	−0.503434	−	0.405366i
$409$	9.81463	+	5.66648i	0.485302	+	0.280189i	0.722623	−	0.691242i	$-0.242936\pi$
$409$	9.81463	+	5.66648i	0.485302	+	0.280189i	−0.237321	+	0.971431i	$0.576269\pi$
$410$	−3.60905	−	2.08369i	−0.178238	−	0.102906i
$411$	−22.0707	+	8.54247i	−1.08867	+	0.421369i
$412$	29.3081	+	16.9210i	1.44391	+	0.833639i
$413$	−5.79618	+	6.65380i	−0.285212	+	0.327412i
$414$	−5.86066	−	1.86837i	−0.288035	−	0.0918251i
$415$	2.64187	−	4.57586i	0.129684	−	0.224620i
$416$	−2.54655			−0.124855
$417$	−3.53595	−	2.84715i	−0.173156	−	0.139426i
$418$		−	0.0104766i		−	0.000512428i
$419$	−11.3963	−	19.7389i	−0.556745	−	0.964311i	−0.997765	−	0.0668135i	$-0.978717\pi$
$419$	−11.3963	−	19.7389i	−0.556745	−	0.964311i	0.441021	−	0.897497i	$-0.354617\pi$
$420$	−7.68294	−	2.78126i	−0.374889	−	0.135712i
$421$	−5.98203	+	10.3612i	−0.291546	+	0.504973i	−0.974176	−	0.225792i	$-0.927503\pi$
$421$	−5.98203	+	10.3612i	−0.291546	+	0.504973i	0.682629	+	0.730765i	$0.260836\pi$
$422$	6.95515	+	4.01556i	0.338571	+	0.195474i
$423$	−27.2176	−	8.67690i	−1.32336	−	0.421885i
$424$	−6.39746	−	11.0807i	−0.310688	−	0.538128i
$425$	2.13878	+	3.70447i	0.103746	+	0.179693i
$426$	6.84624	−	8.50251i	0.331701	−	0.411948i
$427$	−27.3455	+	9.38410i	−1.32334	+	0.454128i
$428$	−9.51410	+	5.49297i	−0.459881	+	0.265513i
$429$	−0.115824	+	0.143845i	−0.00559204	+	0.00694489i
$430$			4.24818i			0.204865i
$431$	−21.0311	+	12.1423i	−1.01303	+	0.584874i	−0.912078	−	0.410017i	$-0.865523\pi$
$431$	−21.0311	+	12.1423i	−1.01303	+	0.584874i	−0.100954	+	0.994891i	$0.532190\pi$
$432$	0.865059	+	14.2385i	0.0416202	+	0.685049i
$433$		−	20.1695i		−	0.969285i	−0.874712	−	0.484643i	$-0.838950\pi$
$433$		−	20.1695i		−	0.969285i	0.874712	−	0.484643i	$-0.161050\pi$
$434$	−6.41940	−	1.25471i	−0.308141	−	0.0602281i
$435$	0.374014	−	2.40457i	0.0179326	−	0.115290i
$436$	2.27567			0.108985
$437$	0.246156	−	0.426354i	0.0117752	−	0.0203953i
$438$	−3.53639	−	0.550059i	−0.168975	−	0.0262828i
$439$	10.3064	−	5.95040i	0.491897	−	0.283997i	−0.233464	−	0.972365i	$-0.575006\pi$
$439$	10.3064	−	5.95040i	0.491897	−	0.283997i	0.725361	+	0.688368i	$0.241673\pi$
$440$	0.354375			0.0168942
$441$	−19.7085	+	7.25092i	−0.938499	+	0.345282i
$442$	1.05641			0.0502485
$443$	34.7308	−	20.0519i	1.65011	−	0.952692i	0.673087	−	0.739563i	$-0.264968\pi$
$443$	34.7308	−	20.0519i	1.65011	−	0.952692i	0.977024	−	0.213129i	$-0.0683655\pi$
$444$	3.16699	−	3.93316i	0.150299	−	0.186660i
$445$	2.74526	−	4.75493i	0.130138	−	0.225405i
$446$	0.680522			0.0322236
$447$	9.32434	−	3.60898i	0.441026	−	0.170699i
$448$	−8.44740	−	1.65110i	−0.399102	−	0.0780071i
$449$			29.9614i			1.41396i	0.707231	+	0.706982i	$0.249944\pi$
$449$			29.9614i			1.41396i	−0.707231	+	0.706982i	$0.750056\pi$
$450$	−0.424444	+	1.33139i	−0.0200085	+	0.0627622i
$451$	−1.55816	+	0.899606i	−0.0733711	+	0.0423608i
$452$		−	25.4793i		−	1.19844i
$453$	−6.33546	−	16.3686i	−0.297666	−	0.769064i
$454$	−7.90378	+	4.56325i	−0.370943	+	0.214164i
$455$	1.32682	−	0.455321i	0.0622021	−	0.0213458i
$456$	0.337294	+	0.0524636i	0.0157952	+	0.00245683i
$457$	−1.51838	−	2.62991i	−0.0710268	−	0.123022i	0.828325	−	0.560248i	$-0.189294\pi$
$457$	−1.51838	−	2.62991i	−0.0710268	−	0.123022i	−0.899352	+	0.437226i	$0.855961\pi$
$458$	−4.40864	−	7.63599i	−0.206002	−	0.356806i
$459$	−1.34791	−	22.1859i	−0.0629150	−	1.03555i
$460$	6.79721	+	3.92437i	0.316922	+	0.182975i
$461$	−11.0626	+	19.1611i	−0.515239	+	0.892420i	0.484605	+	0.874733i	$0.338963\pi$
$461$	−11.0626	+	19.1611i	−0.515239	+	0.892420i	−0.999844	+	0.0176867i	$0.994370\pi$
$462$	0.328362	−	0.276502i	0.0152768	−	0.0128640i
$463$	−4.48360	−	7.76583i	−0.208371	−	0.360909i	0.742831	−	0.669479i	$-0.233483\pi$
$463$	−4.48360	−	7.76583i	−0.208371	−	0.360909i	−0.951201	+	0.308571i	$0.900149\pi$
$464$		−	3.85700i		−	0.179057i
$465$	1.41288	−	9.08353i	0.0655205	−	0.421239i
$466$	3.98483			0.184594
$467$	−17.6976	+	30.6531i	−0.818947	+	1.41846i	0.0875119	+	0.996163i	$0.472108\pi$
$467$	−17.6976	+	30.6531i	−0.818947	+	1.41846i	−0.906459	+	0.422294i	$0.861225\pi$
$468$	−1.90936	−	2.09705i	−0.0882602	−	0.0969361i
$469$	13.7580	−	15.7937i	0.635287	−	0.729286i
$470$	−3.84130	−	2.21778i	−0.177186	−	0.102298i
$471$	−5.43215	+	34.9239i	−0.250300	+	1.60921i
$472$	5.08984	+	2.93862i	0.234279	+	0.135261i
$473$	1.58838	+	0.917050i	0.0730337	+	0.0421660i
$474$	2.13985	−	13.7573i	0.0982865	−	0.631894i
$475$	−0.0968564	−	0.0559201i	−0.00444408	−	0.00256579i
$476$	19.8044	+	3.87090i	0.907734	+	0.177423i
$477$	6.61630	−	20.7539i	0.302940	−	0.950256i
$478$	5.47639	−	9.48539i	0.250484	−	0.433852i
$479$	−37.9159			−1.73242			−0.866210	−	0.499681i	$-0.833451\pi$
$479$	−37.9159			−1.73242			−0.866210	+	0.499681i	$0.833451\pi$
$480$	−1.27860	+	8.22024i	−0.0583597	+	0.375201i
$481$			0.866931i			0.0395286i
$482$	5.11338	+	8.85663i	0.232908	+	0.403408i
$483$	19.8595	−	3.53735i	0.903640	−	0.160955i
$484$	−9.77060	+	16.9232i	−0.444118	+	0.769235i
$485$	−0.347490	−	0.200623i	−0.0157787	−	0.00910983i
$486$	5.06270	−	5.20510i	0.229649	−	0.236108i
$487$	7.39195	+	12.8032i	0.334961	+	0.580170i	0.983477	−	0.181031i	$-0.0579435\pi$
$487$	7.39195	+	12.8032i	0.334961	+	0.580170i	−0.648516	+	0.761201i	$0.724610\pi$
$488$	9.62770	+	16.6757i	0.435825	+	0.754872i
$489$	−38.6755	−	6.01568i	−1.74897	−	0.272039i
$490$	−3.22982	+	0.447093i	−0.145908	+	0.0201976i
$491$	−17.2983	+	9.98718i	−0.780662	+	0.450715i	−0.836665	−	0.547715i	$-0.815498\pi$
$491$	−17.2983	+	9.98718i	−0.780662	+	0.450715i	0.0560030	+	0.998431i	$0.482164\pi$
$492$	−9.97318	−	25.7672i	−0.449626	−	1.16167i
$493$			6.00986i			0.270671i
$494$	−0.0239203	+	0.0138104i	−0.00107622	+	0.000621359i
$495$	0.406176	+	0.446103i	0.0182563	+	0.0200508i
$496$		−	14.5702i		−	0.654223i
$497$	−6.86701	+	35.1332i	−0.308028	+	1.57594i
$498$	−3.97550	+	1.53871i	−0.178146	+	0.0689515i
$499$	−0.906111			−0.0405631			−0.0202815	−	0.999794i	$-0.506456\pi$
$499$	−0.906111			−0.0405631			−0.0202815	+	0.999794i	$0.506456\pi$
$500$	0.891514	−	1.54415i	0.0398697	−	0.0690564i
$501$	5.33725	−	6.62845i	0.238451	−	0.296138i
$502$	−4.12340	+	2.38064i	−0.184036	+	0.106253i
$503$	18.0100			0.803024			0.401512	−	0.915854i	$-0.368485\pi$
$503$	18.0100			0.803024			0.401512	+	0.915854i	$0.368485\pi$
$504$	7.25762	+	11.9562i	0.323280	+	0.532572i
$505$	−8.29113			−0.368950
$506$	−0.357105	+	0.206175i	−0.0158752	+	0.00916558i
$507$	−21.7680	−	3.38585i	−0.966752	−	0.150371i
$508$	14.6936	−	25.4501i	0.651924	−	1.12917i
$509$	2.93715			0.130187			0.0650933	−	0.997879i	$-0.479265\pi$
$509$	2.93715			0.130187			0.0650933	+	0.997879i	$0.479265\pi$
$510$	0.530416	−	3.41010i	0.0234872	−	0.151002i
$511$	11.1010	−	3.80952i	0.491080	−	0.168523i
$512$			22.8605i			1.01030i
$513$	0.320555	+	0.484733i	0.0141529	+	0.0214015i
$514$	8.15294	−	4.70710i	0.359611	−	0.207621i
$515$			18.9801i			0.836363i
$516$	−17.6645	+	21.9379i	−0.777634	+	0.965763i
$517$	−1.65844	+	0.957498i	−0.0729379	+	0.0421107i
$518$	0.386551	−	1.97768i	0.0169841	−	0.0868945i
$519$	−6.32339	+	7.85318i	−0.277566	+	0.344716i
$520$	−0.467141	−	0.809111i	−0.0204855	−	0.0354819i
$521$	11.5754	+	20.0492i	0.507129	+	0.878373i	0.999966	+	0.00825135i	$0.00262652\pi$
$521$	11.5754	+	20.0492i	0.507129	+	0.878373i	−0.492837	+	0.870122i	$0.664040\pi$
$522$	−1.45172	+	1.32179i	−0.0635401	+	0.0578532i
$523$	22.3972	+	12.9310i	0.979361	+	0.565434i	0.902077	−	0.431575i	$-0.142042\pi$
$523$	22.3972	+	12.9310i	0.979361	+	0.565434i	0.0772838	+	0.997009i	$0.475375\pi$
$524$	−16.7829	+	29.0689i	−0.733166	+	1.26988i
$525$	−0.803592	−	4.51157i	−0.0350716	−	0.196901i
$526$	−1.04337	−	1.80718i	−0.0454933	−	0.0787967i
$527$			22.7029i			0.988953i
$528$	0.744799	+	0.599714i	0.0324132	+	0.0260992i
$529$	3.62313			0.157527
$530$	1.69110	−	2.92906i	0.0734565	−	0.127230i
$531$	2.13459	+	9.77551i	0.0926334	+	0.424221i
$532$	−0.499034	+	0.171253i	−0.0216359	+	0.00742474i
$533$	4.10798	+	2.37174i	0.177936	+	0.102732i
$534$	−4.13108	+	1.59893i	−0.178769	+	0.0691925i
$535$	−5.33592	−	3.08069i	−0.230692	−	0.133190i
$536$	−12.0814	−	6.97523i	−0.521839	−	0.301284i
$537$	7.56969	+	6.09513i	0.326656	+	0.263024i
$538$	−3.12045	−	1.80159i	−0.134532	−	0.0776721i
$539$	−0.530051	+	1.30413i	−0.0228309	+	0.0561728i
$540$	−7.72793	+	5.11050i	−0.332557	+	0.219921i
$541$	1.65707	−	2.87012i	0.0712428	−	0.123396i	−0.828203	−	0.560428i	$-0.810637\pi$
$541$	1.65707	−	2.87012i	0.0712428	−	0.123396i	0.899446	+	0.437031i	$0.143970\pi$
$542$	2.19577			0.0943163
$543$	−4.00969	+	1.55195i	−0.172072	+	0.0666006i
$544$		−	20.5452i		−	0.880869i
$545$	0.638147	+	1.10530i	0.0273352	+	0.0473460i
$546$	−1.06416	−	0.385231i	−0.0455419	−	0.0164864i
$547$	−7.17011	+	12.4190i	−0.306572	+	0.530998i	−0.977610	−	0.210425i	$-0.932515\pi$
$547$	−7.17011	+	12.4190i	−0.306572	+	0.530998i	0.671038	+	0.741423i	$0.265849\pi$
$548$	−21.0988	−	12.1814i	−0.901296	−	0.520364i
$549$	−9.95703	+	31.2330i	−0.424956	+	1.33299i
$550$	0.0468375	+	0.0811248i	0.00199716	+	0.00345918i
$551$	−0.0785663	−	0.136081i	−0.00334704	−	0.00579724i
$552$	−4.84951	−	12.5294i	−0.206409	−	0.533287i
$553$	14.8198	+	43.1854i	0.630204	+	1.83643i
$554$	3.03652	−	1.75313i	0.129009	−	0.0744835i
$555$	2.79845	+	0.435278i	0.118788	+	0.0184765i
$556$		−	4.67335i		−	0.198194i
$557$	23.8667	−	13.7795i	1.01127	−	0.583855i	0.0997042	−	0.995017i	$-0.468210\pi$
$557$	23.8667	−	13.7795i	1.01127	−	0.583855i	0.911562	+	0.411162i	$0.134877\pi$
$558$	−5.48403	+	4.99320i	−0.232157	+	0.211379i
$559$		−	4.83546i		−	0.204518i
$560$	−2.35756	−	6.86998i	−0.0996250	−	0.290310i
$561$	−1.16052	−	0.934455i	−0.0489973	−	0.0394527i
$562$	−2.35204			−0.0992147
$563$	−8.66051	+	15.0004i	−0.364997	+	0.632193i	−0.988776	−	0.149408i	$-0.952263\pi$
$563$	−8.66051	+	15.0004i	−0.364997	+	0.632193i	0.623779	+	0.781601i	$0.285597\pi$
$564$	−10.6150	−	27.4254i	−0.446971	−	1.15482i
$565$	12.3754	−	7.14494i	0.520637	−	0.300590i
$566$	−2.88864			−0.121419
$567$	−6.73252	+	22.8402i	−0.282739	+	0.959197i
$568$	23.8425			1.00041
$569$	−17.7647	+	10.2565i	−0.744736	+	0.429974i	−0.823789	−	0.566897i	$-0.808144\pi$
$569$	−17.7647	+	10.2565i	−0.744736	+	0.429974i	0.0790527	+	0.996870i	$0.474810\pi$
$570$	0.0325697	+	0.0841487i	0.00136420	+	0.00352460i
$571$	13.9189	−	24.1082i	0.582487	−	1.00890i	−0.412696	−	0.910869i	$-0.635413\pi$
$571$	13.9189	−	24.1082i	0.582487	−	1.00890i	0.995184	−	0.0980287i	$-0.0312537\pi$
$572$	−0.190115			−0.00794911
$573$	12.9715	+	10.4447i	0.541894	+	0.436334i
$574$	−8.31379	−	7.24222i	−0.347011	−	0.302284i
$575$			4.40192i			0.183573i
$576$	−7.21654	+	6.57065i	−0.300689	+	0.273777i
$577$	13.8385	−	7.98965i	0.576103	−	0.332613i	−0.183480	−	0.983023i	$-0.558736\pi$
$577$	13.8385	−	7.98965i	0.576103	−	0.332613i	0.759583	+	0.650410i	$0.225403\pi$
$578$			0.604383i			0.0251390i
$579$	22.0128	+	3.42393i	0.914821	+	0.142294i
$580$	2.16949	−	1.25255i	0.0900831	−	0.0520095i
$581$	9.18230	−	10.5409i	0.380946	−	0.437311i
$582$	0.116850	+	0.301898i	0.00484358	+	0.0125141i
$583$	−0.730110	−	1.26459i	−0.0302381	−	0.0523739i
$584$	−3.90841	−	6.76957i	−0.161731	−	0.280127i
$585$	0.483120	−	1.51544i	0.0199746	−	0.0626558i
$586$	7.23332	+	4.17616i	0.298806	+	0.172516i
$587$	20.7440	−	35.9296i	0.856196	−	1.48297i	−0.0193354	−	0.999813i	$-0.506155\pi$
$587$	20.7440	−	35.9296i	0.856196	−	1.48297i	0.875531	−	0.483162i	$-0.160512\pi$
$588$	−18.5381	−	11.1212i	−0.764498	−	0.458629i
$589$	−0.296792	−	0.514060i	−0.0122291	−	0.0211815i
$590$			1.55358i			0.0639600i
$591$	27.2084	−	10.5310i	1.11920	−	0.433188i
$592$	4.48879			0.184488
$593$	9.14878	−	15.8461i	0.375695	−	0.650723i	−0.614736	−	0.788733i	$-0.710737\pi$
$593$	9.14878	−	15.8461i	0.375695	−	0.650723i	0.990431	+	0.138010i	$0.0440706\pi$
$594$	−0.0295180	−	0.485853i	−0.00121114	−	0.0199348i
$595$	3.67347	+	10.7046i	0.150598	+	0.438845i
$596$	8.91372	+	5.14634i	0.365120	+	0.210802i
$597$	−17.4267	−	14.0321i	−0.713229	−	0.574294i
$598$	0.941479	+	0.543563i	0.0384999	+	0.0222279i
$599$	−1.97139	−	1.13818i	−0.0805487	−	0.0465048i	0.459185	−	0.888341i	$-0.348142\pi$
$599$	−1.97139	−	1.13818i	−0.0805487	−	0.0465048i	−0.539733	+	0.841836i	$0.681475\pi$
$600$	−2.84636	+	1.10168i	−0.116202	+	0.0449759i
$601$	14.3810	+	8.30287i	0.586613	+	0.338681i	0.763757	−	0.645504i	$-0.223353\pi$
$601$	14.3810	+	8.30287i	0.586613	+	0.338681i	−0.177144	+	0.984185i	$0.556686\pi$
$602$	−2.15606	+	11.0309i	−0.0878744	+	0.449585i
$603$	−5.06675	−	23.2035i	−0.206334	−	0.944920i
$604$	9.03424	−	15.6478i	0.367598	−	0.636699i
$605$	−10.9596			−0.445569
$606$	5.21016	+	4.19523i	0.211648	+	0.170420i
$607$			1.06089i			0.0430603i	0.999768	+	0.0215301i	$0.00685378\pi$
$607$			1.06089i			0.0430603i	−0.999768	+	0.0215301i	$0.993146\pi$
$608$	0.268586	+	0.465204i	0.0108926	+	0.0188665i
$609$	2.19155	−	6.05393i	0.0888062	−	0.245318i
$610$	−2.54497	+	4.40802i	−0.103043	+	0.178475i
$611$	4.37234	+	2.52437i	0.176886	+	0.102125i
$612$	16.9187	−	15.4045i	0.683899	−	0.622689i
$613$	11.5936	+	20.0806i	0.468260	+	0.811050i	0.999342	−	0.0362706i	$-0.0115478\pi$
$613$	11.5936	+	20.0806i	0.468260	+	0.811050i	−0.531082	+	0.847320i	$0.678214\pi$
$614$	−6.16097	−	10.6711i	−0.248637	−	0.430651i
$615$	9.71855	−	12.0697i	0.391890	−	0.486697i
$616$	0.920176	+	0.179854i	0.0370749	+	0.00724654i
$617$	−21.7510	+	12.5579i	−0.875661	+	0.505563i	−0.869225	−	0.494416i	$-0.835382\pi$
$617$	−21.7510	+	12.5579i	−0.875661	+	0.505563i	−0.00643595	+	0.999979i	$0.502049\pi$
$618$	9.60375	−	11.9271i	0.386319	−	0.479779i
$619$		−	29.2150i		−	1.17425i	−0.809496	−	0.587125i	$-0.800260\pi$
$619$		−	29.2150i		−	1.17425i	0.809496	−	0.587125i	$-0.199740\pi$
$620$	8.19547	−	4.73166i	0.329138	−	0.190028i
$621$	10.2142	−	20.4657i	0.409882	−	0.821261i
$622$			3.91521i			0.156986i
$623$	9.54164	−	10.9534i	0.382278	−	0.438841i
$624$	0.387469	−	2.49108i	0.0155112	−	0.0997230i
$625$	1.00000			0.0400000
$626$	6.99165	−	12.1099i	0.279443	−	0.484009i
$627$	0.0384937	+	0.00598740i	0.00153729	+	0.000239114i
$628$	−31.5095	+	18.1920i	−1.25737	+	0.725941i
$629$	−6.99429			−0.278881
$630$	−1.77783	+	3.24169i	−0.0708305	+	0.129152i
$631$	24.8121			0.987756			0.493878	−	0.869531i	$-0.335579\pi$
$631$	24.8121			0.987756			0.493878	+	0.869531i	$0.335579\pi$
$632$	26.3351	−	15.2046i	1.04755	−	0.604805i
$633$	−18.7290	+	23.2600i	−0.744412	+	0.924503i
$634$	3.81723	−	6.61163i	0.151601	−	0.262581i
$635$	16.4817			0.654055
$636$	20.9124	−	8.09412i	0.829229	−	0.320953i
$637$	3.67632	−	0.508901i	0.145661	−	0.0201634i
$638$			0.131611i			0.00521052i
$639$	27.3277	+	30.0140i	1.08107	+	1.18733i
$640$	−9.63143	+	5.56071i	−0.380716	+	0.219806i
$641$		−	23.9688i		−	0.946709i	−0.880872	−	0.473355i	$-0.843043\pi$
$641$		−	23.9688i		−	0.946709i	0.880872	−	0.473355i	$-0.156957\pi$
$642$	1.79430	+	4.63584i	0.0708153	+	0.182962i
$643$	−2.59262	+	1.49685i	−0.102243	+	0.0590300i	−0.550250	−	0.835000i	$-0.685467\pi$
$643$	−2.59262	+	1.49685i	−0.102243	+	0.0590300i	0.448007	+	0.894030i	$0.352134\pi$
$644$	15.6580	+	13.6398i	0.617013	+	0.537485i
$645$	−15.6088	−	2.42784i	−0.614598	−	0.0955961i
$646$	−0.111421	−	0.192986i	−0.00438378	−	0.00759294i
$647$	−12.9789	−	22.4801i	−0.510254	−	0.883785i	−0.999929	−	0.0118806i	$-0.996218\pi$
$647$	−12.9789	−	22.4801i	−0.510254	−	0.883785i	0.489676	−	0.871905i	$-0.337115\pi$
$648$	15.7898	+	1.48267i	0.620283	+	0.0582447i
$649$	0.580878	+	0.335370i	0.0228015	+	0.0131644i
$650$	0.123483	−	0.213879i	0.00484341	−	0.00838903i
$651$	8.27882	−	22.8694i	0.324473	−	0.896321i
$652$	−20.1463	−	34.8943i	−0.788988	−	1.36657i
$653$		−	27.7167i		−	1.08464i	−0.840173	−	0.542318i	$-0.817547\pi$
$653$		−	27.7167i		−	1.08464i	0.840173	−	0.542318i	$-0.182453\pi$
$654$	0.158260	−	1.01747i	0.00618845	−	0.0397862i
$655$	−18.8252			−0.735562
$656$	12.2804	−	21.2703i	0.479469	−	0.830464i
$657$	4.04211	−	12.6792i	0.157698	−	0.494663i
$658$	−8.84881	−	7.70827i	−0.344962	−	0.300500i
$659$	10.8467	+	6.26232i	0.422526	+	0.243946i	0.696157	−	0.717889i	$-0.254892\pi$
$659$	10.8467	+	6.26232i	0.422526	+	0.243946i	−0.273631	+	0.961835i	$0.588225\pi$
$660$	−0.0954551	+	0.613691i	−0.00371558	+	0.0238879i
$661$	−40.0716	−	23.1353i	−1.55860	−	0.899861i	−0.997391	−	0.0721898i	$-0.977001\pi$
$661$	−40.0716	−	23.1353i	−1.55860	−	0.899861i	−0.561214	−	0.827671i	$-0.689665\pi$
$662$	−8.15420	−	4.70783i	−0.316922	−	0.182975i
$663$	−0.603742	+	3.88152i	−0.0234474	+	0.150746i
$664$	−8.06331	−	4.65536i	−0.312917	−	0.180663i
$665$	−0.223118	−	0.194360i	−0.00865215	−	0.00753696i
$666$	−1.53830	−	1.68952i	−0.0596081	−	0.0654675i
$667$	−3.09229	+	5.35600i	−0.119734	+	0.207385i
$668$	8.76062			0.338958
$669$	−0.388919	+	2.50040i	−0.0150365	+	0.0966712i
$670$		−	3.68764i		−	0.142466i
$671$	1.09876	+	1.90311i	0.0424172	+	0.0734687i
$672$	−7.49201	+	20.6959i	−0.289011	+	0.798362i
$673$	−14.3805	+	24.9077i	−0.554327	+	0.960122i	0.443629	+	0.896210i	$0.353691\pi$
$673$	−14.3805	+	24.9077i	−0.554327	+	0.960122i	−0.997956	+	0.0639112i	$0.979643\pi$
$674$	−2.68216	−	1.54855i	−0.103313	−	0.0596477i
$675$	−4.64927	−	2.32040i	−0.178951	−	0.0893122i
$676$	−11.3391	−	19.6399i	−0.436118	−	0.755379i
$677$	16.4970	+	28.5737i	0.634032	+	1.09818i	0.986719	+	0.162434i	$0.0519345\pi$
$677$	16.4970	+	28.5737i	0.634032	+	1.09818i	−0.352688	+	0.935741i	$0.614732\pi$
$678$	−11.3920	−	1.77194i	−0.437507	−	0.0680510i
$679$	−0.800476	−	0.697302i	−0.0307195	−	0.0267600i
$680$	6.52781	−	3.76883i	0.250330	−	0.144528i
$681$	−12.2495	−	31.6483i	−0.469401	−	1.21277i
$682$			0.497174i			0.0190378i
$683$	9.80815	−	5.66274i	0.375298	−	0.216679i	−0.300472	−	0.953791i	$-0.597144\pi$
$683$	9.80815	−	5.66274i	0.375298	−	0.216679i	0.675771	+	0.737112i	$0.263811\pi$
$684$	−0.181708	+	0.569979i	−0.00694779	+	0.0217937i
$685$		−	13.6637i		−	0.522064i
$686$	−8.61351	−	0.478285i	−0.328865	−	0.0182610i
$687$	30.5760	−	11.8344i	1.16655	−	0.451512i
$688$	−25.0370			−0.954527
$689$	−1.92488	+	3.33399i	−0.0733320	+	0.127015i
$690$	2.22733	−	2.76617i	0.0847929	−	0.105306i
$691$	18.7896	−	10.8482i	0.714790	−	0.412684i	−0.0980421	−	0.995182i	$-0.531258\pi$
$691$	18.7896	−	10.8482i	0.714790	−	0.412684i	0.812832	+	0.582498i	$0.197925\pi$
$692$	−10.3793			−0.394562
$693$	0.828276	+	1.36450i	0.0314636	+	0.0518332i
$694$	7.63174			0.289697
$695$	2.26987	−	1.31051i	0.0861010	−	0.0497104i
$696$	−4.23720	−	0.659065i	−0.160611	−	0.0249818i
$697$	−19.1349	+	33.1427i	−0.724787	+	1.25537i
$698$	13.5577			0.513166
$699$	−2.27734	+	14.6412i	−0.0861368	+	0.553782i
$700$	3.09862	−	3.55709i	0.117117	−	0.134446i
$701$		−	25.3422i		−	0.957162i	−0.878043	−	0.478581i	$-0.841151\pi$
$701$		−	25.3422i		−	0.957162i	0.878043	−	0.478581i	$-0.158849\pi$
$702$	−1.07039	+	0.707853i	−0.0403994	+	0.0267162i
$703$	0.158371	−	0.0914357i	0.00597309	−	0.00344856i
$704$			0.654240i			0.0246576i
$705$	10.3440	−	12.8464i	0.389576	−	0.483824i
$706$	−3.86495	+	2.23143i	−0.145459	+	0.0839809i
$707$	−21.5289	−	4.20796i	−0.809677	−	0.158257i
$708$	−6.45999	+	8.02282i	−0.242781	+	0.301516i
$709$	10.0095	+	17.3370i	0.375916	+	0.651106i	0.990464	−	0.137774i	$-0.0439947\pi$
$709$	10.0095	+	17.3370i	0.375916	+	0.651106i	−0.614548	+	0.788880i	$0.710661\pi$
$710$	3.15124	+	5.45811i	0.118264	+	0.204839i
$711$	49.3248	+	15.7247i	1.84983	+	0.589721i
$712$	−8.37887	−	4.83754i	−0.314011	−	0.181295i
$713$	−11.6815	+	20.2329i	−0.437474	+	0.757727i
$714$	3.10800	−	8.58552i	0.116314	−	0.321305i
$715$	−0.0533124	−	0.0923398i	−0.00199377	−	0.00345331i
$716$			10.0046i			0.373890i
$717$	31.7219	+	25.5425i	1.18468	+	0.953904i
$718$	11.8978			0.444023
$719$	12.6142	−	21.8484i	0.470430	−	0.814808i	−0.528999	−	0.848623i	$-0.677432\pi$
$719$	12.6142	−	21.8484i	0.470430	−	0.814808i	0.999428	+	0.0338148i	$0.0107656\pi$
$720$	−7.84665	−	2.50150i	−0.292427	−	0.0932253i
$721$	−9.63289	+	49.2840i	−0.358747	+	1.83543i
$722$	−7.65949	−	4.42221i	−0.285057	−	0.164577i
$723$	−35.4637	+	13.7262i	−1.31891	+	0.510484i
$724$	−3.83312	−	2.21305i	−0.142457	−	0.0822474i
$725$	1.21674	+	0.702487i	0.0451887	+	0.0260897i
$726$	6.88700	+	5.54543i	0.255601	+	0.205810i
$727$	−29.7303	−	17.1648i	−1.10263	−	0.636606i	−0.165722	−	0.986172i	$-0.552996\pi$
$727$	−29.7303	−	17.1648i	−1.10263	−	0.636606i	−0.936912	+	0.349566i	$0.886329\pi$
$728$	−0.802340	−	2.33804i	−0.0297367	−	0.0866534i
$729$	16.2315	+	21.5763i	0.601166	+	0.799124i
$730$	1.03314	−	1.78946i	0.0382384	−	0.0662308i
$731$	39.0119			1.44291
$732$	−31.4715	+	12.1810i	−1.16322	+	0.450224i
$733$			14.1051i			0.520984i	0.965476	+	0.260492i	$0.0838848\pi$
$733$			14.1051i			0.520984i	−0.965476	+	0.260492i	$0.916115\pi$
$734$	−1.36923	−	2.37157i	−0.0505392	−	0.0875364i
$735$	0.203115	−	12.1227i	0.00749200	−	0.447151i
$736$	10.5713	−	18.3100i	0.389662	−	0.674914i
$737$	−1.37880	−	0.796048i	−0.0507886	−	0.0293228i
$738$	−12.2143	+	2.66713i	−0.449615	+	0.0981784i
$739$	20.0137	+	34.6648i	0.736216	+	1.27516i	0.954188	+	0.299209i	$0.0967226\pi$
$739$	20.0137	+	34.6648i	0.736216	+	1.27516i	−0.217972	+	0.975955i	$0.569944\pi$
$740$	1.45773	+	2.52486i	0.0535871	+	0.0928156i
$741$	−0.0370723	−	0.0957817i	−0.00136188	−	0.00351863i
$742$	5.87770	−	6.74738i	0.215777	−	0.247704i
$743$	23.5123	−	13.5748i	0.862583	−	0.498013i	−0.00229341	−	0.999997i	$-0.500730\pi$
$743$	23.5123	−	13.5748i	0.862583	−	0.498013i	0.864876	+	0.501985i	$0.167397\pi$
$744$	−16.0065	−	2.48969i	−0.586826	−	0.0912764i
$745$			5.77258i			0.211491i
$746$	0.119743	−	0.0691337i	0.00438411	−	0.00253116i
$747$	−3.38161	−	15.4863i	−0.123727	−	0.566615i
$748$		−	1.53383i		−	0.0560822i
$749$	−12.2918	−	10.7075i	−0.449133	−	0.391244i
$750$	−0.628402	−	0.505990i	−0.0229460	−	0.0184762i
$751$	35.1343			1.28207			0.641034	−	0.767512i	$-0.278506\pi$
$751$	35.1343			1.28207			0.641034	+	0.767512i	$0.278506\pi$
$752$	13.0707	−	22.6391i	0.476638	−	0.825561i
$753$	−6.39054	−	16.5109i	−0.232884	−	0.601691i
$754$	0.300495	−	0.173491i	0.0109434	−	0.00631816i
$755$	10.1336			0.368799
$756$	−22.6602	+	9.34788i	−0.824143	+	0.339979i
$757$	−31.2076			−1.13426			−0.567130	−	0.823628i	$-0.691946\pi$
$757$	−31.2076			−1.13426			−0.567130	+	0.823628i	$0.691946\pi$
$758$	5.55439	−	3.20683i	0.201745	−	0.116477i
$759$	−0.553450	−	1.42992i	−0.0200890	−	0.0519028i
$760$	−0.0985392	+	0.170675i	−0.00357439	+	0.00619103i
$761$	−28.4234			−1.03035			−0.515173	−	0.857086i	$-0.672272\pi$
$761$	−28.4234			−1.03035			−0.515173	+	0.857086i	$0.672272\pi$
$762$	−10.3571	−	8.33956i	−0.375198	−	0.302110i
$763$	1.09605	+	3.19392i	0.0396798	+	0.115628i
$764$			17.1441i			0.620251i
$765$	12.2264	+	3.89775i	0.442047	+	0.140924i
$766$	−15.2365	+	8.79682i	−0.550519	+	0.317842i
$767$		−	1.76835i		−	0.0638516i
$768$	−2.26956	−	0.353014i	−0.0818959	−	0.0127383i
$769$	−12.2541	+	7.07489i	−0.441893	+	0.255127i	−0.704400	−	0.709803i	$-0.748784\pi$
$769$	−12.2541	+	7.07489i	−0.441893	+	0.255127i	0.262507	+	0.964930i	$0.415451\pi$
$770$	0.0804460	+	0.234421i	0.00289907	+	0.00844796i
$771$	12.6356	+	32.6460i	0.455061	+	1.17572i
$772$	11.4666	+	19.8607i	0.412691	+	0.714802i
$773$	−23.1844	−	40.1566i	−0.833886	−	1.44433i	−0.894934	−	0.446199i	$-0.852777\pi$
$773$	−23.1844	−	40.1566i	−0.833886	−	1.44433i	0.0610476	−	0.998135i	$-0.480556\pi$
$774$	8.58016	+	9.42358i	0.308407	+	0.338724i
$775$	4.59638	+	2.65372i	0.165107	+	0.0953244i
$776$	−0.353527	+	0.612326i	−0.0126909	+	0.0219812i
$777$	7.04559	+	2.55054i	0.252759	+	0.0914999i
$778$	−4.74186	−	8.21315i	−0.170004	−	0.294456i
$779$		−	1.00060i		−	0.0358501i
$780$	1.52701	−	0.591030i	0.0546759	−	0.0211623i
$781$	2.72102			0.0973658
$782$	−4.38540	+	7.59574i	−0.156822	+	0.271623i
$783$	−4.02692	−	6.08939i	−0.143910	−	0.217617i
$784$	−2.63499	−	19.0352i	−0.0941066	−	0.679829i
$785$	−17.6719	−	10.2029i	−0.630738	−	0.364157i
$786$	11.8298	+	9.52537i	0.421955	+	0.339759i
$787$	21.5944	+	12.4675i	0.769757	+	0.444419i	0.832788	−	0.553592i	$-0.186743\pi$
$787$	21.5944	+	12.4675i	0.769757	+	0.444419i	−0.0630310	+	0.998012i	$0.520077\pi$
$788$	26.0102	+	15.0170i	0.926576	+	0.534959i
$789$	7.23630	−	2.80081i	0.257619	−	0.0997114i
$790$	6.96137	+	4.01915i	0.247674	+	0.142995i
$791$	35.7604	−	12.2718i	1.27149	−	0.436336i
$792$	0.786097	−	0.715741i	0.0279328	−	0.0254327i
$793$	2.89680	−	5.01740i	0.102868	−	0.178173i
$794$	7.16620			0.254319
$795$	9.79563	+	7.88746i	0.347415	+	0.279740i
$796$		−	23.0324i		−	0.816361i
$797$	6.60338	+	11.4374i	0.233904	+	0.405133i	0.958954	−	0.283563i	$-0.0915166\pi$
$797$	6.60338	+	11.4374i	0.233904	+	0.405133i	−0.725050	+	0.688697i	$0.758183\pi$
$798$	0.0418635	+	0.235032i	0.00148195	+	0.00832004i
$799$	−20.3663	+	35.2755i	−0.720508	+	1.24796i
$800$	−4.15954	−	2.40151i	−0.147062	−	0.0849063i
$801$	−3.51395	−	16.0924i	−0.124159	−	0.568596i
$802$	1.96294	+	3.39991i	0.0693137	+	0.120055i
$803$	−0.446047	−	0.772577i	−0.0157407	−	0.0272636i
$804$	15.3337	−	19.0433i	0.540777	−	0.671604i
$805$	−2.23409	+	11.4301i	−0.0787412	+	0.402858i
$806$	1.13515	−	0.655380i	0.0399840	−	0.0230848i
$807$	8.40283	−	10.4357i	0.295794	−	0.367353i
$808$			14.6102i			0.513983i
$809$	−46.3028	+	26.7330i	−1.62792	+	0.939881i	−0.643209	+	0.765691i	$0.722397\pi$
$809$	−46.3028	+	26.7330i	−1.62792	+	0.939881i	−0.984712	+	0.174190i	$0.944269\pi$
$810$	1.74751	+	3.81063i	0.0614013	+	0.133892i
$811$		−	51.2248i		−	1.79875i	−0.437181	−	0.899373i	$-0.644023\pi$
$811$		−	51.2248i		−	1.79875i	0.437181	−	0.899373i	$-0.355977\pi$
$812$	6.26903	−	2.15133i	0.220000	−	0.0754970i
$813$	−1.25488	+	8.06779i	−0.0440107	+	0.282950i
$814$	−0.153169			−0.00536857
$815$	11.2989	−	19.5703i	0.395783	−	0.685517i
$816$	20.0977	+	3.12605i	0.703561	+	0.109434i
$817$	−0.883344	+	0.509999i	−0.0309043	+	0.0178426i
$818$	5.27891			0.184573
$819$	2.02360	−	3.68983i	0.0707104	−	0.128933i
$820$	15.9521			0.557073
$821$	−34.3913	+	19.8558i	−1.20026	+	0.692973i	−0.960614	−	0.277886i	$-0.910366\pi$
$821$	−34.3913	+	19.8558i	−1.20026	+	0.692973i	−0.239650	+	0.970859i	$0.577033\pi$
$822$	−6.91371	+	8.58630i	−0.241143	+	0.299482i
$823$	−21.7417	+	37.6577i	−0.757867	+	1.31266i	0.186070	+	0.982537i	$0.440425\pi$
$823$	−21.7417	+	37.6577i	−0.757867	+	1.31266i	−0.943936	+	0.330127i	$0.892908\pi$
$824$	33.4456			1.16513
$825$	−0.324840	+	0.125729i	−0.0113095	+	0.00437733i
$826$	−0.788483	+	4.03406i	−0.0274348	+	0.140363i
$827$			16.7140i			0.581203i	0.956844	+	0.290601i	$0.0938553\pi$
$827$			16.7140i			0.581203i	−0.956844	+	0.290601i	$0.906145\pi$
$828$	23.0042	−	5.02322i	0.799450	−	0.174569i
$829$	9.09104	−	5.24872i	0.315745	−	0.182295i	−0.333749	−	0.942662i	$-0.608314\pi$
$829$	9.09104	−	5.24872i	0.315745	−	0.182295i	0.649494	+	0.760366i	$0.274981\pi$
$830$		−	2.46118i		−	0.0854288i
$831$	4.70607	+	12.1588i	0.163252	+	0.421785i
$832$	1.49377	−	0.862426i	0.0517870	−	0.0298993i
$833$	4.10575	+	29.6601i	0.142256	+	1.02766i
$834$	−2.08949	−	0.325005i	−0.0723532	−	0.0112540i
$835$	2.45667	+	4.25507i	0.0850165	+	0.147253i
$836$	0.0200516	+	0.0347303i	0.000693497	+	0.00120117i
$837$	−15.2121	−	23.0033i	−0.525808	−	0.795110i
$838$	−9.19444	−	5.30841i	−0.317617	−	0.183376i
$839$	1.83656	−	3.18101i	0.0634050	−	0.109821i	−0.832580	−	0.553904i	$-0.813137\pi$
$839$	1.83656	−	3.18101i	0.0634050	−	0.109821i	0.895985	+	0.444084i	$0.146471\pi$
$840$	−7.95002	+	1.41604i	−0.274302	+	0.0488582i
$841$	−13.5130	−	23.4052i	−0.465966	−	0.807077i
$842$			5.57288i			0.192054i
$843$	1.34419	−	8.64196i	0.0462965	−	0.297645i
$844$	−30.7420			−1.05818
$845$	6.35945	−	11.0149i	0.218772	−	0.378924i
$846$	−13.0003	+	2.83877i	−0.446960	+	0.0975988i
$847$	−28.4578	−	5.56226i	−0.977820	−	0.191121i
$848$	17.2627	+	9.96662i	0.592804	+	0.342255i
$849$	1.65086	−	10.6136i	0.0566575	−	0.364257i
$850$	1.72555	+	0.996248i	0.0591859	+	0.0341710i
$851$	−6.23333	−	3.59882i	−0.213676	−	0.123366i
$852$	−6.42225	+	41.2893i	−0.220023	+	1.41455i
$853$	24.2274	+	13.9877i	0.829530	+	0.478930i	0.853692	−	0.520778i	$-0.174358\pi$
$853$	24.2274	+	13.9877i	0.829530	+	0.478930i	−0.0241615	+	0.999708i	$0.507692\pi$
$854$	−8.84550	+	10.1543i	−0.302687	+	0.347473i
$855$	−0.327797	+	0.0715780i	−0.0112104	+	0.00244792i
$856$	−5.42862	+	9.40265i	−0.185547	+	0.321376i
$857$	−9.75546			−0.333240			−0.166620	−	0.986021i	$-0.553285\pi$
$857$	−9.75546			−0.333240			−0.166620	+	0.986021i	$0.553285\pi$
$858$	−0.0132214	+	0.0850021i	−0.000451373	+	0.00290192i
$859$			25.0437i			0.854481i	0.904138	+	0.427240i	$0.140514\pi$
$859$			25.0437i			0.854481i	−0.904138	+	0.427240i	$0.859486\pi$
$860$	−8.13073	−	14.0828i	−0.277256	−	0.480221i
$861$	31.3610	−	26.4080i	1.06878	−	0.899981i
$862$	−5.65591	+	9.79633i	−0.192641	+	0.333664i
$863$	−40.0494	−	23.1225i	−1.36330	−	0.787100i	−0.373236	−	0.927736i	$-0.621752\pi$
$863$	−40.0494	−	23.1225i	−1.36330	−	0.787100i	−0.990061	+	0.140636i	$0.955085\pi$
$864$	13.7664	+	20.8171i	0.468342	+	0.708212i
$865$	−2.91058	−	5.04127i	−0.0989627	−	0.171408i
$866$	−4.69750	−	8.13631i	−0.159628	−	0.276483i
$867$	−2.22065	−	0.345406i	−0.0754173	−	0.0117306i
$868$	23.6819	−	8.12689i	0.803817	−	0.275845i
$869$	3.00549	−	1.73522i	0.101954	−	0.0588633i
$870$	−0.409152	−	1.05710i	−0.0138715	−	0.0358392i
$871$			4.19743i			0.142225i
$872$	1.94770	−	1.12451i	0.0659575	−	0.0380806i
$873$	−1.17603	+	0.256799i	−0.0398025	+	0.00869133i
$874$		−	0.229320i		−	0.00775685i
$875$	2.59662	+	0.507526i	0.0877817	+	0.0171575i
$876$	12.7760	−	4.94495i	0.431662	−	0.167074i
$877$	−1.28832			−0.0435036			−0.0217518	−	0.999763i	$-0.506924\pi$
$877$	−1.28832			−0.0435036			−0.0217518	+	0.999763i	$0.506924\pi$
$878$	2.77171	−	4.80074i	0.0935406	−	0.162017i
$879$	−19.4781	+	24.1903i	−0.656980	+	0.815919i
$880$	−0.478117	+	0.276041i	−0.0161173	+	0.00930533i
$881$	5.41086			0.182296			0.0911482	−	0.995837i	$-0.470946\pi$
$881$	5.41086			0.182296			0.0911482	+	0.995837i	$0.470946\pi$
$882$	−6.26158	+	7.51512i	−0.210838	+	0.253047i
$883$	3.84672			0.129452			0.0647262	−	0.997903i	$-0.479383\pi$
$883$	3.84672			0.129452			0.0647262	+	0.997903i	$0.479383\pi$
$884$	−3.50204	+	2.02191i	−0.117786	+	0.0680040i
$885$	−5.70824	−	0.887875i	−0.191880	−	0.0298456i
$886$	9.34019	−	16.1777i	0.313790	−	0.543500i
$887$	−4.00387			−0.134437			−0.0672183	−	0.997738i	$-0.521412\pi$
$887$	−4.00387			−0.134437			−0.0672183	+	0.997738i	$0.521412\pi$
$888$	0.767022	−	4.93127i	0.0257396	−	0.165482i
$889$	42.7965	+	8.36486i	1.43535	+	0.280549i
$890$		−	2.55750i		−	0.0857275i
$891$	1.80201	+	0.169209i	0.0603697	+	0.00566873i
$892$	−2.25595	+	1.30247i	−0.0755348	+	0.0436100i
$893$		−	1.06499i		−	0.0356384i
$894$	2.92087	−	3.62750i	0.0976885	−	0.121322i
$895$	−4.85929	+	2.80551i	−0.162428	+	0.0937779i
$896$	−27.8313	+	9.55083i	−0.929780	+	0.319071i
$897$	−2.53524	+	3.14858i	−0.0846492	+	0.105128i
$898$	6.97804	+	12.0863i	0.232860	+	0.403326i
$899$	3.72841	+	6.45779i	0.124349	+	0.215379i
$900$	−1.14114	−	5.22595i	−0.0380381	−	0.174198i
$901$	−26.8982	−	15.5297i	−0.896109	−	0.517369i
$902$	−0.419039	+	0.725796i	−0.0139525	+	0.0241664i
$903$	−39.2980	−	14.2261i	−1.30776	−	0.473414i
$904$	−12.5904	−	21.8072i	−0.418751	−	0.725298i
$905$		−	2.48235i		−	0.0825161i
$906$	−6.36797	−	5.12750i	−0.211562	−	0.170350i
$907$	−17.0074			−0.564720			−0.282360	−	0.959308i	$-0.591117\pi$
$907$	−17.0074			−0.564720			−0.282360	+	0.959308i	$0.591117\pi$
$908$	17.4675	−	30.2546i	0.579680	−	1.00404i
$909$	−18.3919	+	16.7458i	−0.610022	+	0.555424i
$910$	0.429188	−	0.492691i	0.0142274	−	0.0163326i
$911$	−31.3148	−	18.0796i	−1.03751	−	0.599004i	−0.118380	−	0.992968i	$-0.537770\pi$
$911$	−31.3148	−	18.0796i	−1.03751	−	0.599004i	−0.919126	+	0.393964i	$0.871103\pi$
$912$	−0.495938	+	0.191953i	−0.0164221	+	0.00635619i
$913$	−0.920226	−	0.531293i	−0.0304550	−	0.0175832i
$914$	−1.22502	−	0.707264i	−0.0405200	−	0.0233942i
$915$	−14.7417	−	11.8700i	−0.487345	−	0.392411i
$916$	29.2295	+	16.8757i	0.965771	+	0.557588i
$917$	−48.8819	−	9.55428i	−1.61422	−	0.315510i
$918$	−5.71087	−	8.63580i	−0.188487	−	0.285024i
$919$	−25.9263	+	44.9057i	−0.855231	+	1.48130i	0.0211991	+	0.999775i	$0.493252\pi$
$919$	−25.9263	+	44.9057i	−0.855231	+	1.48130i	−0.876430	+	0.481529i	$0.840082\pi$
$920$	7.75680			0.255734
$921$	42.7293	−	16.5384i	1.40798	−	0.544958i
$922$			10.3060i			0.339410i
$923$	−3.58688	−	6.21265i	−0.118063	−	0.204492i
$924$	−0.559324	+	1.54507i	−0.0184004	+	0.0508292i
$925$	−0.817557	+	1.41605i	−0.0268811	+	0.0465594i
$926$	−3.61734	−	2.08847i	−0.118873	−	0.0686314i
$927$	38.3346	+	42.1029i	1.25907	+	1.38284i
$928$	−3.37407	−	5.84405i	−0.110759	−	0.191840i
$929$	−11.0404	−	19.1226i	−0.362224	−	0.627391i	0.626102	−	0.779741i	$-0.284649\pi$
$929$	−11.0404	−	19.1226i	−0.362224	−	0.627391i	−0.988327	+	0.152350i	$0.951316\pi$
$930$	−1.54561	−	3.99332i	−0.0506827	−	0.130946i
$931$	−0.480710	−	0.617917i	−0.0157546	−	0.0202514i
$932$	−13.2098	+	7.62670i	−0.432702	+	0.249821i
$933$	−14.3854	−	2.23755i	−0.470958	−	0.0732540i
$934$			16.4872i			0.539476i
$935$	0.744987	−	0.430118i	0.0243637	−	0.0140664i
$936$	−2.67043	−	0.851326i	−0.0872856	−	0.0278265i
$937$		−	38.1387i		−	1.24594i	−0.782247	−	0.622968i	$-0.785927\pi$
$937$		−	38.1387i		−	1.24594i	0.782247	−	0.622968i	$-0.214073\pi$
$938$	1.87157	−	9.57539i	0.0611090	−	0.312648i
$939$	40.4990	+	32.6099i	1.32163	+	1.06418i
$940$	16.9787			0.553784
$941$	−26.8147	+	46.4444i	−0.874134	+	1.51404i	−0.0164514	+	0.999865i	$0.505237\pi$
$941$	−26.8147	+	46.4444i	−0.874134	+	1.51404i	−0.857682	+	0.514180i	$0.828096\pi$
$942$	5.94250	+	15.3533i	0.193617	+	0.500238i
$943$	−34.1062	+	19.6912i	−1.11065	+	0.641234i
$944$	−9.15618			−0.298008
$945$	−10.8947	−	8.38481i	−0.354405	−	0.272758i
$946$	0.854328			0.0277766
$947$	−43.2235	+	24.9551i	−1.40457	+	0.810931i	−0.994858	−	0.101282i	$-0.967706\pi$
$947$	−43.2235	+	24.9551i	−1.40457	+	0.810931i	−0.409716	+	0.912213i	$0.634372\pi$
$948$	19.2369	+	49.7014i	0.624786	+	1.61423i
$949$	−1.17597	+	2.03684i	−0.0381736	+	0.0661185i
$950$	−0.0520954			−0.00169020
$951$	22.1112	+	17.8040i	0.717005	+	0.577334i
$952$	18.8630	−	6.47319i	0.611354	−	0.209797i
$953$		−	46.9332i		−	1.52031i	−0.649739	−	0.760157i	$-0.725122\pi$
$953$		−	46.9332i		−	1.52031i	0.649739	−	0.760157i	$-0.274878\pi$
$954$	−2.16461	−	9.91299i	−0.0700819	−	0.320945i
$955$	−8.32696	+	4.80757i	−0.269454	+	0.155569i
$956$			41.9258i			1.35598i
$957$	−0.483571	−	0.0752158i	−0.0156316	−	0.00243138i
$958$	−15.2951	+	8.83064i	−0.494163	+	0.285305i
$959$	6.93469	−	35.4794i	0.223933	−	1.14569i
$960$	−2.03390	−	5.25489i	−0.0656439	−	0.169601i
$961$	−1.41555	−	2.45180i	−0.0456629	−	0.0790905i
$962$	0.201909	+	0.349717i	0.00650981	+	0.0112753i
$963$	−18.0586	+	3.94331i	−0.581932	+	0.127071i
$964$	−33.9020	−	19.5733i	−1.09191	−	0.630414i
$965$	−6.43096	+	11.1387i	−0.207020	+	0.358569i
$966$	7.18742	−	6.05226i	0.231251	−	0.194728i
$967$	−20.5276	−	35.5548i	−0.660123	−	1.14337i	−0.980583	−	0.196105i	$-0.937171\pi$
$967$	−20.5276	−	35.5548i	−0.660123	−	1.14337i	0.320460	−	0.947262i	$-0.396163\pi$
$968$			19.3123i			0.620721i
$969$	0.772755	−	0.299095i	0.0248245	−	0.00960830i
$970$	−0.186901			−0.00600105
$971$	−12.8786	+	22.3065i	−0.413295	+	0.715849i	−0.995248	−	0.0973741i	$-0.968956\pi$
$971$	−12.8786	+	22.3065i	−0.413295	+	0.715849i	0.581952	+	0.813223i	$0.302289\pi$
$972$	−6.82079	+	26.9448i	−0.218777	+	0.864254i
$973$	6.55909	−	2.25087i	0.210275	−	0.0721597i
$974$	5.96377	+	3.44319i	0.191092	+	0.110327i
$975$	0.715274	+	0.575940i	0.0229071	+	0.0184448i
$976$	−25.9791	−	14.9990i	−0.831570	−	0.480107i
$977$	−26.6825	−	15.4052i	−0.853649	−	0.492855i	0.00823130	−	0.999966i	$-0.497380\pi$
$977$	−26.6825	−	15.4052i	−0.853649	−	0.492855i	−0.861880	+	0.507112i	$0.830713\pi$
$978$	−17.0026	+	6.58086i	−0.543684	+	0.210433i
$979$	−0.956239	−	0.552085i	−0.0305615	−	0.0176447i
$980$	9.85123	−	7.66378i	0.314686	−	0.244811i
$981$	3.64799	+	1.16297i	0.116471	+	0.0371308i
$982$	−4.65205	+	8.05759i	−0.148453	+	0.257128i
$983$	36.2192			1.15521			0.577606	−	0.816316i	$-0.303987\pi$
$983$	36.2192			1.15521			0.577606	+	0.816316i	$0.303987\pi$
$984$	−21.2685	−	17.1255i	−0.678016	−	0.545940i
$985$			16.8444i			0.536707i
$986$	1.39970	+	2.42436i	0.0445756	+	0.0772072i
$987$	33.3792	−	28.1074i	1.06247	−	0.894668i
$988$	0.0528643	−	0.0915637i	0.00168184	−	0.00291303i
$989$	34.7675	+	20.0730i	1.10554	+	0.638285i
$990$	0.267748	+	0.0853575i	0.00850959	+	0.00271284i
$991$	13.0801	+	22.6554i	0.415504	+	0.719674i	0.995481	−	0.0949586i	$-0.0302719\pi$
$991$	13.0801	+	22.6554i	0.415504	+	0.719674i	−0.579977	+	0.814633i	$0.696939\pi$
$992$	−12.7459	−	22.0765i	−0.404682	−	0.700930i
$993$	21.9579	−	27.2700i	0.696812	−	0.865387i
$994$	5.41243	+	15.7719i	0.171672	+	0.500256i
$995$	11.1869	−	6.45878i	0.354650	−	0.204757i
$996$	10.2339	−	12.7097i	0.324273	−	0.402723i
$997$		−	12.6540i		−	0.400757i	−0.979719	−	0.200379i	$-0.935783\pi$
$997$		−	12.6540i		−	0.400757i	0.979719	−	0.200379i	$-0.0642172\pi$
$998$	−0.365522	+	0.211034i	−0.0115704	+	0.00668017i
$999$	7.08685	−	4.68654i	0.224218	−	0.148276i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.c.236.10	yes	32
3.2	odd	2		945.2.be.c.656.7		32
7.3	odd	6		315.2.t.c.101.10	✓	32
9.4	even	3		945.2.t.c.341.10		32
9.5	odd	6		315.2.t.c.131.7	yes	32
21.17	even	6		945.2.t.c.521.7		32
63.31	odd	6		945.2.be.c.206.7		32
63.59	even	6	inner	315.2.be.c.311.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.10	✓	32	7.3	odd	6
315.2.t.c.131.7	yes	32	9.5	odd	6
315.2.be.c.236.10	yes	32	1.1	even	1	trivial
315.2.be.c.311.10	yes	32	63.59	even	6	inner
945.2.t.c.341.10		32	9.4	even	3
945.2.t.c.521.7		32	21.17	even	6
945.2.be.c.206.7		32	63.31	odd	6
945.2.be.c.656.7		32	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.403396 - 0.232901i) q^{2} +(0.625194 + 1.61528i) q^{3} +(-0.891514 + 1.54415i) q^{4} -1.00000 q^{5} +(0.628402 + 0.505990i) q^{6} +(-2.59662 - 0.507526i) q^{7} +1.76214i q^{8} +(-2.21827 + 2.01973i) q^{9} +O(q^{10})\)	\(q+(0.403396 - 0.232901i) q^{2} +(0.625194 + 1.61528i) q^{3} +(-0.891514 + 1.54415i) q^{4} -1.00000 q^{5} +(0.628402 + 0.505990i) q^{6} +(-2.59662 - 0.507526i) q^{7} +1.76214i q^{8} +(-2.21827 + 2.01973i) q^{9} +(-0.403396 + 0.232901i) q^{10} +0.201105i q^{11} +(-3.05160 - 0.474654i) q^{12} +(0.459163 - 0.265098i) q^{13} +(-1.16567 + 0.400021i) q^{14} +(-0.625194 - 1.61528i) q^{15} +(-1.37262 - 2.37745i) q^{16} +(2.13878 + 3.70447i) q^{17} +(-0.424444 + 1.33139i) q^{18} +(-0.0968564 - 0.0559201i) q^{19} +(0.891514 - 1.54415i) q^{20} +(-0.803592 - 4.51157i) q^{21} +(0.0468375 + 0.0811248i) q^{22} +4.40192i q^{23} +(-2.84636 + 1.10168i) q^{24} +1.00000 q^{25} +(0.123483 - 0.213879i) q^{26} +(-4.64927 - 2.32040i) q^{27} +(3.09862 - 3.55709i) q^{28} +(1.21674 + 0.702487i) q^{29} +(-0.628402 - 0.505990i) q^{30} +(4.59638 + 2.65372i) q^{31} +(-4.15954 - 2.40151i) q^{32} +(-0.324840 + 0.125729i) q^{33} +(1.72555 + 0.996248i) q^{34} +(2.59662 + 0.507526i) q^{35} +(-1.14114 - 5.22595i) q^{36} +(-0.817557 + 1.41605i) q^{37} -0.0520954 q^{38} +(0.715274 + 0.575940i) q^{39} -1.76214i q^{40} +(4.47333 + 7.74803i) q^{41} +(-1.37492 - 1.63279i) q^{42} +(4.56007 - 7.89827i) q^{43} +(-0.310535 - 0.179288i) q^{44} +(2.21827 - 2.01973i) q^{45} +(1.02521 + 1.77572i) q^{46} +(4.76120 + 8.24664i) q^{47} +(2.98210 - 3.70354i) q^{48} +(6.48484 + 2.63570i) q^{49} +(0.403396 - 0.232901i) q^{50} +(-4.64662 + 5.77074i) q^{51} +0.945355i q^{52} +(-6.28821 + 3.63050i) q^{53} +(-2.41592 + 0.146780i) q^{54} -0.201105i q^{55} +(0.894333 - 4.57561i) q^{56} +(0.0297726 - 0.191411i) q^{57} +0.654440 q^{58} +(1.66764 - 2.88844i) q^{59} +(3.05160 + 0.474654i) q^{60} +(9.46329 - 5.46363i) q^{61} +2.47222 q^{62} +(6.78505 - 4.11863i) q^{63} +3.25323 q^{64} +(-0.459163 + 0.265098i) q^{65} +(-0.101757 + 0.126374i) q^{66} +(-3.95838 + 6.85611i) q^{67} -7.62701 q^{68} +(-7.11033 + 2.75205i) q^{69} +(1.16567 - 0.400021i) q^{70} -13.5304i q^{71} +(-3.55905 - 3.90890i) q^{72} +(-3.84167 + 2.21799i) q^{73} +0.761639i q^{74} +(0.625194 + 1.61528i) q^{75} +(0.172698 - 0.0997071i) q^{76} +(0.102066 - 0.522191i) q^{77} +(0.422676 + 0.0657441i) q^{78} +(-8.62845 - 14.9449i) q^{79} +(1.37262 + 2.37745i) q^{80} +(0.841400 - 8.96058i) q^{81} +(3.60905 + 2.08369i) q^{82} +(-2.64187 + 4.57586i) q^{83} +(7.68294 + 2.78126i) q^{84} +(-2.13878 - 3.70447i) q^{85} -4.24818i q^{86} +(-0.374014 + 2.40457i) q^{87} -0.354375 q^{88} +(-2.74526 + 4.75493i) q^{89} +(0.424444 - 1.33139i) q^{90} +(-1.32682 + 0.455321i) q^{91} +(-6.79721 - 3.92437i) q^{92} +(-1.41288 + 9.08353i) q^{93} +(3.84130 + 2.21778i) q^{94} +(0.0968564 + 0.0559201i) q^{95} +(1.27860 - 8.22024i) q^{96} +(0.347490 + 0.200623i) q^{97} +(3.22982 - 0.447093i) q^{98} +(-0.406176 - 0.446103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

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